3 digit numbers divisible by 6 The idea is to express the n digit numbers in powers of 10. What is the smallest six digit number divisible by 4? The smallest 6-digit number divisible by 4 is 100000. What we want to check is whether 3 can be divided by 6 without any remainder (i. Largest three-digit number that is exactly divisible Welcome to The Divisibility Rules for 3, 6 and 9 (4 Digit Numbers) (A) Math Worksheet from the Division Worksheets Page at Math-Drills. Also, given X + Y ≤ 5, Thus, to satisfy the above two conditions, (X + Y) is either equal to 2 or 5, Also, X cannot be equal to 0, otherwise the number will not be a 5-digit number We know that the divisibility test of 6 states that a number is divisible by 6 if the number is even and the sum of the digits is divisible by 3. A number is divisible by 6 if it is divisible by both 2 and 3. Hence, 120 is the smallest 3-digit integer evenly divisible by both 5 and 6. Calculation: First three-digit number divisible by 6, (a) = 102 . If the last digit of a number is 6 then is 6 a factor? Not necessarily. Solution: The last number of the given number is 0. 2 | 3 15 21 12. This math worksheet was created or last revised on 2013-02-14 and has been Find five numbers in A. e the answer is a whole number). Select odd only, even only, half odd and half even or custom number of odd/even. 3 | 3 15 21 3 Here, 4, 3, 6 and 8 are the digits of the number 4368. Solve. Hence, the largest six digit number divisible by 24, 15 and 36 = 999999 − 279 VIDEO ANSWER: Most people's end of their will is three in order to be divided by six. [6 \times 17 = 102] So, the smallest 3-digit number divisible by 6 is 102. permutations; Share. We can see that the sum of the digits in this case is 6 and this number IS divisible by 3, which means that 6 is also divisible by 3. The three digit numbers divisible by 6 are 1 0 2, 1 0 8, 1 1 4,. Share on Whatsapp Finding the First 3-Digit Number Divisible by 6: The smallest 3-digit number is 100. Note that 255 is not an even number (any number ending in 0, 2, 4, 6, or 8) which makes it not divisible 2. Correct option is B) Lets you pick 5 numbers between 1 and 100. What is the smallest six digit number divisible by 6? To find the largest 4-digit number and smallest 3-digit number divisible by 6, 15, 21, and 24, you first have to find the least common multiple (LCM) of the four numbers since any number divisible by all four must be a multiple of their LCM. Difference between two consecutive numbers divisible Number of numbers divisible by 6 from 1 to 999 : 999 ÷ 6 = 166. There are 150 three digit numbers divisible by 6. (vi) first 8 multiples of 3. 1 5 0. . This Question Belongs to Arithmetic Ability >> Number System. 900 / 6 = 150, hence, there will be 150 positive three-digit numbers (integers) divisible by 6. So, basically, any odd number or any number that doesn't have 2 or 3 as a factor won't be cozy with 6. Q1. Last three-digit number divisible by 6, (a n) = 996. a n = a + (n − 1) d 96=12+(n-1)6 84=(n-1)6 n-1=14 n=15 hence total no of two digits no. Example: 630, the number is divisible by 2 as the last digit is 0. ⇒ sum of digits = k + 5 + 3 + 2 + 0 + 6 + k = 16 + 2k . 6 = 6. What is the smallest three digit number divisible by 23? The smallest or lowest 3-digit number divisible by 23 is the first number on the list above (first 3 digit number divisible by 23). three digit numbers) which are divisible by six. How many 3 digit numbers are divisible by 6 in all? A. He attempts 30 questions and gets 40 marks. How many $3$ digit numbers can be formed using digits $1,2,3,4$ and $5$ without repetition such that the number is divisible by $6$ First Approach: A number is divisible by $6$ if it is divisible Divisibility rule of 3: If the sum of digits is divisible by 3, we say that the original number is divisible by 3. For example, Let us check whether the following numbers are divisible by 3: 345, 796, 6125, 321, 506 The digits of a 3 - digit number are in AP, and their sum is 15. Complete step-by-step answer: We know, Step 1: Condition for divisibility by 6. This math worksheet was created or last revised on 2017-05-29 and has been viewed 187 times this week and 287 times this month. What is the largest three digit number divisible by 7? The largest or greatest 3-digit number divisible by 7 is the last number on the list above (last 3 digit number divisible by 7). Numbers are divisible by 4 if the last two digits of the number are divisible by 4. 150 4. Free Tests. Olivia decides to increase her character’s Attack. You can generalize it to n digit numbers. Find the sum of all the three digit natural numbers which on division by 7 leaves remainder 3. Verified by Toppr. The sum of the digits is divisible by 3. To check this, the last digit must be even and the sum of the digits must be divisible by three. M. What is the number of 5 digit numbers divisible by 3 and number 6 in it? I have been thinking of counting all 5 digit numbers that have 6 in it and divide it by 3. whose sum is `12 1/2` and the ratio of the first to the last terms is 2 : 3. Long division, large numbers. As 6 = 2 x 3, thus the product must be multiple of 6. View all Free tests > Free. For Now, the greatest six digit number which is divisible by 24, 15 and 36 should be a multiple of LCM of 24, 15, 36. 12 = 2 2 × 3 . Concept used: The greatest number of 3 digits is 999. A whole number is said to be divisible by 3 if the sum of all digits of that whole number is a multiple of 3 or exactly divisible by 3. Hence, 100002 is the smallest number divisible by 6 as it is even and the sum of digits 1 + 0 + 0 + 0 + 0 + 2 = 3. First 3 Digit Number Exactly Divisible by 6. $$150$$ C. LCM = 2 × 2 × 2 × 3 × 3 × 5 = 360. Because 1001 is divisible by seven, an interesting pattern develops for repeating sets of 1, 2, or 3 digits that form 6-digit numbers (leading zeros are allowed [A number is divisible by 3, if the sum of its digits is a multiple of 3 or divisibility by 3]. asked Jul 23, 2021 in Arithmetic Progression by Haifa ( 50. How many 3 digit numbers are completely d Is the following number divisible by 3: 7,218, 6155, 2,096, and 3,342. The number obtained by reversing the digits is 594 less than the original number. Reason: A number of divisible by 4, if the last two digits of the number are divisible by 4. shaalaa. Generate numbers sorted in ascending order or unsorted. The sum of three numbers in A. The last digits of Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is___. The correct option is B 150. Therefore, there are 50 three-digit numbers divisible by 3 and 6 For this, we must find out the first three digit number divisible by 6. e. We know the divisibility rule for 3: If the sum of the digits of a number is divisible by 3, then the number is also divisible by 3. C. There are $\lfloor\frac{999}{6}\rfloor - \lfloor\frac{99}{6}\rfloor$ numbers between $100$ and $999$ (i. Can repeat this if needed, Example: 286. It may be printed, downloaded or saved and To find how many three-digit numbers are divisible by 6, we need to follow these steps: Step 1: Identify the range of three-digit numbers The smallest three-digit number is 100, and the largest three-digit number is 999. The prime factorization of 6 is 2*3, of 15 is 3*5, of 21 is 3*7, and of 24 is 23*3. Finding the last three-digit number divisible by 6: The largest three-digit number is 999. the answer is not 20) The largest 4 digit number is 9240 and smallest 3 digit number is 840. Each digit appearing only once in each number, how many of these will be : (a) divisible by 5 (b) divisible by 25 (c) odd (e) greater than 50,000. If sum of digits of number is divisible by 3 or multiple of 3 42 is divisible by 3. Odd numbers are not. Free | Worksheets | Math Drills | Division | Printable Long division, remainders, 6-digit by 3-digit Buy Workbook. any rules ?? To check the divisibility by 3 we add all the digits 1, 3, 6, 5, 8, and 2 which will result in 25 which is not divisible by 3. 1, 2, and 3 times 30 each produce a 2-digit number. How many number of ways can this be done ? If it asked for numbers divisible by $2$, I know how to proceed -- the last digit could be $0, 2$ or $4$. The greatest 3 digit number 9A6 is divisible by 6. 196 2. Well, honey, any number that doesn't end in 0, 2, 3, 4, 6, or 8 is not divisible by 6. → 999 divided by 6 gives 3 as remainder. 249 is not divisible by 2 because the last digit, 9, is not even. So, it is not divisible by 2 and hence not divisible by 6. Since 999 is ⇒ The number should be an even number and sum of its digits should be divisible by 3. D. Often, this is an easiest calculation to How many two-digit numbers are divisible by 6? [CBSE 2011] View Solution Lets say your 2 digit number is AB. Open in App. So,all these number are divisible by $3$. D 97. , 9 9 6 We have a = 1 0 2, a n How many six digit numbers are divisible by 6? Yes, we counted all the 6-digit numbers divisible by 6. And finally, 121 is the smallest 3-digit integer when divided by either 5 or 6 How many 3-digit numbers are exactly divisible by 6? 140; 150; 160; 170; Answer (Detailed Solution Below) Option 2 : 150. The divisibility rules for 3 and 9 are quite similar. Example of divisibility rule for 6: Consider the number 47394. This is an if and only if statement. We have to include all odd numbers, so we have to cross out all of the numbers that are on that. Solution: The sum of the digits in the number 46 * 8782 = 4 + 6+ 8 + 7 + 8 + 2 = 35 (i) The number next to 35 which is divisible by 3 = 36. Now, Thus, the remainder obtained is 279. The number 7,218 is divisible by 3 because: 7 + 2 + 1 + 8 = 18; 18 ÷ 3 = 6, meaning 18 is divisible by 3 into an integer. AI Homework Helper; Math Solver; 9 2 How many 3 digit numbers are divisible by 6 in all (A) 149 (B) 150 (C) 151 (D Find the sum of the digits of the smallest 6-digit number divisible by 120. Divisibility by 3. The largest integer contained in 166. divisible by 6 = 15 The sum of all 3-digit numbers divisible by 23 is 21528. Five digit number divisible by $3$ is formed using $0,1,2,3,4,6$ and $7$ without repetition. If the sum of these digits is divisible by 3, the number would also be divisible by 3. Example: 138 is divisible by 2 because the last digit, 8, is even. Finding the Last 3-Digit Number Divisible by 6: The 3-digit numbers divisible by 6 are 102, 108, 114 . So the number 136582 is not divisible by 6. To find the first 3 digit To find three-digit numbers divisible by 6, we need to find the first and last three-digit multiples of 6. So, 996 is the largest number divisible by 3. 5 is 16. Solution Show Solution. Now, let us divide the last three digit number by 6. The number are 4, 5 and 6. There are 150000 six digit numbers divisible by 6. Since number is to be divisible by 6 meaning it need to be divisible by 2 and 3. The smallest six-digit number is 100000. in which a = 102, d = 6 and T n = 996 ∴ T n = a + (n - 1) d ⇒ 102 + (n - 1) × 6 = 996 ⇒ (n - 1) × 6 = 894 ⇒ (n - 1) = 149 ⇒ n = 150 . Calculations: LCM of 3, 4, 5, and 8 = 120. 3 digit no divisible by 6 are 102,108,114,. Therefore, the series is 102, 108, 114, . Numbers which are divisible by both 2 and 3 are divisible by 6. Download Solution PDF. 217 (2+1+7=10, and 10÷3 = 3 1 / 3) No. Note: Any six-digit number is formed by writing a three digit number two-times, that number is always divisible by 1001 and its prime factors 7, 11 and 13. The number 6,155 is not (ii) the first 40 positive integers divisible by (a) 3 (b) 5 (c) 6. If word start with 0 we put 6 on the left of it , and if word start with non zero digit then we can place 6 in $(4-1)+2 = 5 $ places. ,996. Multiply 4 by 0 and add to the rest of the number. Now we will divide the smallest-3 digit number with the LCM obtained, and the remainder will be subtracted from the dividend, and 24 will be added to it to make it The smallest 6-digit number is 100000. For divisibility by 12, the number should be divisible by 3 and 4. Also, its sum of digits is 4 + 7 + 3 + 9 + 4 = 27. in which a = 102, d = 6 and T n = 996 ∴ T n = a + (n - 1) d ⇒ 102 + (n - 1) × 6 = 996 ⇒ (n - 1) × 6 = 894 ⇒ (n - 1) = To calculate the number of 3-digit numbers is divisible by 6, substitute the obtained smallest and largest 3-digit number value in the formula. Multiples of 24 = 24, 48, 72, 96, 120, 144 Clearly, 120 is the smallest 3-digit multiple of 24. Find the numbers. What is the smallest three digit number divisible by 3? The smallest or lowest 3-digit number divisible by 3 is the first number on the list above (first 3 digit number divisible by 3). The sum of all 3-digit numbers divisible by 3 is 165150. 1 6 6. So you will have a limited number of situations to analyze. Clearly, 999 - 3 = 996 is the maximum possible three digit number multiple of 6. Therefore, number of 3 digit numbers which are What are numbers that are divisible by 6? Numbers are divisible by 6 if they are divisible by both 2 and 3. 997 The total number of 3-digit numbers divisible by 6 using the digits 1-5 with repetition is obtained by counting combinations where the last digit is 2 or 4 and the sum of all digits is a multiple of 3, resulting in 40 possible numbers. A five digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. 59382 is divisible by 2, and 27 is divisible by 3, so we know it's divisible by 6. 2 24, 15, 36 2 12, 15, 18 2 6, 15, 9 3 3, 15, 9 3 1, 5, 3 5 1, 5, 1 1. Therefore multiply 24 with 5. Divisibility rule for 6 states that a number is divisible by 6 if it is divisible by both 2 and 3. As the test can be repeated on the sum, repeat the summing until a single Tricks to Divide a 3-digit Number by a 2-digit. Numbers are divisible by 2 if they end in 2, 4, 6, 8 or 0. 1 What is the unit digit in 7105 (A) 1 (B) 5 (C) 7 (D) 9 2 How many 3 digit numbers are divisible by 6 in all (A) 149 (B) 150 (C) 151 (D) 166 3 A 3-digit number 4 a 3 is added to another 3 -digit number 984 to give a 4 -digit number 13 b 8 = 2 3. 297 is divisible by 3. Crack UP Lekhpal with. To check whether 3 is divisible by 6, we can simplify it down and check whether 3 is divisible by both 3 and 2. Numbers are divisible by 5 if the last digit of the number is either 5 or 0. That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6. Separate numbers by space, comma, new line or no-space. in this same math how can i solve . Sum of the digits of 100800 = 1 + 0 + 0 + 8 + 0 + 0 = 9. It is not an even number. I don't know where I am going wrong. A number is divisible by 5 if the last digit of the number is 0 or 5. Among the three consecutive numbers, there must be one even number and one multiple of 3. How many three digit natural numbers are divisible by 6 leaving a remainder 2. Find the product of the digits of the largest 4-digit number divisible by 12, 18 and 27. Follow How many five digit numbers are divisible by three and also contain $6$ as one of its digit? My attempt We have to find out four digit "word"( a four digit number that can start with 0 ) divisible by three. 70. ← Prev Question Next Question →. For example, the number 56 ends in a 6 but is not divisible by six. The first two digit no. For example, the sum of the digits for the number 3627 is 18, which is evenly divisible by 3 but 3627 is an odd number Welcome to The 6-Digit by 3-Digit Long Division with Remainders and Steps Shown on Answer Key (A) Math Worksheet from the Division Worksheets Page at Math-Drills. divisible by 6 is 96 So let a=12 ,d=6, a n =96 Now we know that. More Number System Questions . Is 501105 divisible by 2 3 5 9 10? To determine if a number is divisible by another number, you need to check if the first number can be divided by the second number without leaving a remainder. of a, b, and c also divides Divisibility by 3: The sum of digits of the number must be divisible by \(3\). Download & Print Only $5. As you can see, that number is 115. We know that the 3-digit numbers divisible by 6, form an Arithmetic Progression. The n th term of a sequence is 8 – 5n. 5 is 166. 3. ⇒ 996 The smallest or lowest 3-digit number divisible by 8 is the first number on the list above (first 3 digit number divisible by 8). So, the largest 3 digit number divisible by 6 is 996. What is the total number of ways in which a 5-digit number divisible by 3 can be formed? # Number System # Number System basic # Number System ShortTricks MockoPedia Number System PRACTICE Q12 : Q 12. Then t n = 996 ∴ a + (n − 1) d = 996 ⇒ 102 + (n − 1) × 6 = 3-digit numbers divisible by 6 are 102, 108, 114 . So, 542 is not divisible by 8. Hence the total number is 8 Find the sum of the digits of the smallest 6-digit number divisible by 120. The maximum possible three digit number is 999. ⇒ 3 digit greatest numbers = 999 - 39 = A number of 6 different digits is to be formed from the digits 3, 4, 5, 6, 7, 8 which can be done in 6 P 6 = 6! = 720 ways. B. Divisibility Rule – Add the digits of the number whose divisibility by 3 is to be checked. As you can see, that number is 104. → If we divide 100 by 6, we get 4 as remainder. Thus, all the multiples of 24 will also be divisible by 6, 8, and 12. Even numbers are always evenly divisible by 2. 2 | 3 15 21 6 . By dividing 100000 by 48, we get the remainder 16. i confused but hare option a. Numbers are evenly divisible by 3 if the sum of all the individual digits is evenly divisible by 3. Mistake Points The value of k cannot be 0 since Finally For the third one greater than 330 we have two ways to achieve this either draw a 4, 5 or 6 for the first digit then we don't care about the others making $3 \times 6 \times 5 = 90$ Alternatively we must draw a 3 for our first digit then 4, 5 or 6 for our second and finally any digit making $1 \times 3 \times 5 = 15$ Given: The numbers are 2, 3, 4, 5, and 6. First, we check if the sum of all the digits is divisible by 3. Demo Classes Available* Explore Supercoaching For FREE. 149 3. Therefore 120 is the smallest three digit number divisible by 6, 8 and 12. Number of three-digit natural numbers divisible by 6 can be found by using the concept of divisibility rules. For example, determining if a number is even is as simple as checking to see if its last digit is 2, 4, 6, 8 or 0. Easy. , 2, 4, 6, or 8. What is the smallest three digit number divisible by 12? The smallest or lowest 3-digit number divisible by 12 is the first number on the list above (first 3 digit number divisible by 12). Download the numbers or copy them to clipboard How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7, and 9 which are divisible by 7 with no repetition of digits? (p. Just remember, 6 is a bit picky when it comes to sharing its love with other numbers. Numbers up to 1 million are divided by numbers up to one thousand; quotients will include remainders. 999 divided by 6 gives us a quotient of 166 with a remainder of 3. , 996 We have a = 102, a n = 996 3-digit number divisible by 6 are: 102, 108, 114,. Here you can find the meaning of The number of 3-digit numbers divisible by 6, is a)149b)166c)150d)151Correct answer is option 'C'. How many three digit numbers are divisible by 6? 1. Now, we can count how many numbers there are between 12 and 99 that are divisible by 3. A divisibility rule is a heuristic for determining whether a positive integer can be evenly divided by another (i. & if a number is divisible by both 2 (i. You visited us 0 times! Enjoying our articles? Unlock Full Access! Question. Consider 998. ∴ The value of k is 4. 2 | 6 15 21 24. The first two digit number is 10, the last two digit number is 99, so there are 99 - 10 + 1 = 90 two digit numbers → 10 ÷ 3 = 31/3 → first two digit number divisible by 3 is 4 x 3 = 12. So in all cases there are 3 choices for the last digit. Numbers are formed by using all the digits \( 1,2,5,6,9 \). As you can see, that number is 108. Solution For Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1,2,3,4,5 with repetition, is World's only instant tutoring platform. $$102$$ B. there is no remainder left over). A six digit number divisible by $3$ is to be formed using the digits $0,1,2,3,4$ and $5$ without repetition. In the number 46 * 8782, replace * by (i) a smallest digit and (ii) a largest digit to make it divisible by 3. The sum of all 3-digit numbers divisible by 12 is 41400. Furthermore, 900 - 150 = 750. But I have no idea how to do this problem. Hint: Here, we will first try to form an arithmetic progression of the three digit numbers which are divisible by 6. Therefore, 297 is divisible by both 3 but not by 2. all 2 − digit natural numbers divisible by 4. Multiple divisibility rules applied to the same number in this way can help quickly determine its prime factorization without Therefore x+y+z=0(mod 3), meaning that the sum of the digits is divisible by 3. 6. ; Step 3: Bring down the next digit of the dividend and repeat the process. 151 okay sir , plz tell me . 996 This is an A. Complete step-by-step solution - To find the numbers which are divisible by 6, 8 and 12, the number should also be divisible by the LCM of these three numbers. 0, 2, 4, 6, or 8. First three-digit multiple of 6: @$\begin{align*}6 \times 17 = 102\end{align*}@$ Last three-digit multiple of 6: @$\begin{align*}6 \times 166 = 996\end{align*}@$ Now, we can use the formula for the number of terms in an arithmetic sequence: @$\begin{align*}n = \frac{L - F}{D} + 1\end Let us count all three digit numbers which are divisible by six. Example: (i) 2 × 3 × 4 = 24 How many numbers of 3 digits can be formed with \( 0,2,4,6,8 \) ? 2. But I do not think it'll give the right answer. Divisibility by 6: The number should be divisible by both \(2\) and \(3\). Read more: Multiples; Division; Sum; Divisibility Rule of 3 and 9. Submit. The largest 3-digit number is 999. The least number , which when divided by 4, 5 and 6 leaves remainder 1, 2 and 3 respectively is . The number will be 996 and A = 9. Common difference, (d) = 6 (Since the numbers are divisible by 6) Now, a n = a + (n – 1)d. So, sum of digits need to be multiple of 3 and unit digit should be an even number. For 8, the rule is that the last three digits should be divisible by 8. And a number is divisible by 6 if it is divisible by 2 (even number) and by 3. Hailey Hailey Numbers are evenly divisible by 6 if they are evenly divisible by both 2 AND 3. If that number is divisible by 11 then the original number is, too. ⇒ 996 = 102 + (n – 1) × 6 . Number of numbers divisible by 6 from 1 to 99 : 99 ÷ 6 = 16. Solution: Solution: Sum of any three consecutive odd numbers divisible by 3 >> How many 3 digit numbers are divisible b. View Solution; If the total of the first 4 digits is a multiple of 3, then the last digit must be 0, 3 or 9. P. Numbers are divisible by 3 if the sum of their digits is divisible by 3. Now let's consider the two conditions separately:Condition 1: Divisibility by 2For a number to be divisible by 2, its units digit must be an even number (0, 2, 4, 6, or 8). Share. The greatest number of 3 digits = 999. This is sometimes also referred to as the first six digit number divisible by 4 or the lowest 6-digit number divisible by 4. So, LCM (4, 8, 12, 16) = 2 4 × 3 = 48 . Let n be the no of terms then Click here 👆 to get an answer to your question ️smallest 1-digit number to be added to the 6-digit number 726490 so that it is completely divisible by 11 is A) 4 B) 3 C) 8 D) 5 Correct Ans D 13/12/2024 Right. 1 4 9. To find the smallest 3-digit number possible we have to look for smallest 3-digit multiples of 24. View Solution. A number is divisible 6 if it is divisible by both 2 and 3. Study tools. UP Lekhpal General Knowledge (Mock Test) A number is divisible by 2 if the last digit of the given number is 0, 2, 4, 6, or 8. The smallest multiple of 1800 greater than or equal to 100000 is 100800. Divisibility by 4: The number formed by the tens and units digit of the number must be divisible by \(4\). Divisibility Rule of 3 with Examples. Question . ; Step 2: Multiply and subtract to get the remainder. A number is divisible by 2 if the last digit of the given number is 0, 2, 4, 6, or 8. A number is said to be divisible by 6 when the number is divisible by both 2 and 3. As you can see, that number is 105. → 33 - 4 + 1 = 30 two digit numbers divisible by 3 → 10 ÷ 5 = 2 → first two digit number divisible by 5 is 2 x 5 = 10 The number of all five digit numbers which are divisible by 4 that can be formed from the digits 0,1,2,3,4 (without repetition) is The smallest or lowest 3-digit number divisible by 7 is the first number on the list above (first 3 digit number divisible by 7). 16 = 2 4. A number is divisible by 9 if the sum of its digits is divisible by 9. → 99 ÷ 3 = 33 → last two digit number divisible by 3 is 33 x 3 = 99. What is the largest two digit number which when divided by 6 and 5 leaves remainder 1 in each case ? A 61. Since the unit place is divisible by 2. ⇒ Reminder = 39. ∴ No. Then, we will use the formula ${{a}_{n}}=a+\left( n-1 \right)d$ to calculate the value of n which is the total number of terms of the AP. A number is divided by $3$,if sum of the digits of the number is divided by $3$ For all these numbers (Sum of digits)=$(0+1++2+3+4+5+6+7+8+9)=45$ is divided by $3$. Sum. Since its units digit is 4, it is divisible by 2. A number is divisible by 3 if the sum of each digit of the number is divisible by 3. What is the smallest 6 digit number divisible by 2 and 3? The number 100,002 is divisible by 3. If A = 9 then the sum of digits will be 24 which is divisible by 3. 6: It is divisible by 2 and by 3. To find the smallest 3-digit number that is exactly divisible by 6, 8, and 12, we will follow these steps: Step 1: Find the Least Common Multiple (LCM) of 6, 8, and 12 To find the LCM, we can use the prime factorization Thus, the least 3-digit number divisible by 6 is 102. Three digit numbers divisible by 3 are 102, 105,. This forms an AP with ist term,a=102 and common diff,d=6 & last term=996. Next number = 102 + 6 = 108. (a) If the number is to be divisible by 5 Out of the 225000 6-digit numbers divisible by 4, 225000 are even numbers and 0 are odd numbers. Below are the Steps to Divide a 3-digit Number by a 2-digit: Step 1: Estimate the quotient by looking at the first two digits of the dividend and approximating how many times the divisor fits into that number. , 996 We have a = 102, a n = 996. s. Conclusion . Sum of digits $= 6 + 4 + 2 = 12$ 12 is divisible by 3. To check if a number is divisible by six, the number must be divisible by both 2 and 3. FREE. Least 3 digit number divisible by 6 = 96 + 6 = 102. India's Super Teachers. in which a = 102, d = 6, l = 996 Let the number of terms be n. If it gives a remainder 1 when divided by 3, then the last digit must be 2, 5 or 8. , 999 It is nothing but a series of AP whose common difference is 3 and first term is 102 ⇒ A. of three digit numbers which are divisible by 3 is 300. ∴ The largest 3 digit number = 168 × 5 = 840. The three digit numbers divisible by 6 are 102, 108, 114,. In other words, you have a number and you want to know all the 3-digit numbers that when divided by your number will result in a whole number. Precisely, this means: ABABAB = A * 10^5 + B * 10^4 + A * 10^3 + B * 10^2 + A * 10 + B. The sum of three consecutive odd numbers is always divisible by (a) 2 (b) 3 (c) 5 (d) 6. 6 However, the question asks for the number of three-digit numbers divisible by both 3 and 6, which is the same as the number of three-digit numbers divisible by 6. So, we will first find the LCM of 6, 8 and 12. To find the first 3-digit number divisible by 6, we need to find the smallest multiple of 6 that is greater than or equal to 100. For a number to be divisible by 3, the sum of its digits should be divisible by 3, ⇒ Sum of digits = X + Y + 2 + 3 + 5 = X + Y + 10. Cite. Find the product of the digits of the largest 4-digit number divisible by 12, 18 and 27 Divisibility Rule of 6. All whole numbers are divisible by 1. 997 To find the two-digit numbers divisible by 3, we start by finding the first two-digit number divisible by 3, which is 12. When we divide 999 by 6, the remainder will be 3. The divisibility rule for 3 can be understood with the help of the 6 from 49 7 from 49; 3 digit 4 digit; 5 digit 6 digit; Magical Random Numbers; Random numbers that SUM up to a specific value; Random numbers whose DIGITS SUM up to a specific value; Random numbers DIVISIBLE by a specific number; Number Lists - all numbers in sequence; More Lists - all numbers; All Permutations and Combinations; receiptLottery There are 900 three-digit positive integers (starting at 100 and up to 999, i. C. 149 b. The first and also the smallest 3 digit number is 100. 2. Only the numbers where the digits Step by step video & image solution for How many 3-digit numbers are completely divisible by 6? 149 (b) 150 (c) 151 (d) 166 by Maths experts to help you in doubts & scoring excellent marks in Class 14 exams. Subtract the last digit from a number made by the other digits. A number is divisible by 3 if the sum of its figures is a multiple of 3. So, we need to add the difference between the Divisor and Remainder to 100000 (Dividend) in order to get the smallest six-digit number divisible by 48. Here, a → first term, n → Total number, d → common difference, a n → n th term. Click here:point_up_2:to get an answer to your question :writing_hand:how many three digit numbers are divisible by 6 863ab5. As defined above, if the sum of the To be divisible by 6, the number must be divisible by both 2 and 3:To be divisible by 2 the last digit must be even, ie one of {0, 2, 4, 6, 8};To be divisible by 3, sum the digits of the number and if this sum is divisible by 3, then the original number is divisible by 3. Use app Login. [6] 1,458: 1 + 4 + 5 + 8 = 18, so it is divisible by 3 and the last digit is even, hence the number is divisible by 6. Join / Login. If the units place of the number is either 0 or multiple of 2. Pick unique numbers or allow duplicates. $$151$$ D. Find MCQs & Mock Test. Check 3640 for divisibility by 13. Calculation: LCM of 4, 5 and 6 is 60. 9A6 is even and so divisible by 2. This is so because to be divisible by 6, the number should be divisible by both 2 and 3. 9 + 9 + 8 = 26 is not divisible by 3. Guides. Since the sum of the digits of 297 = 2 + 9 + 7 = 18 which is divisible by 3. The largest integer contained in 16. Show that the sequence is an A. 150 d. Solution. How many three digit numbers are NOT divisible by 6? Like we wrote above, there are a total of 900 three digit numbers and 150 of them are divisible by 6. B 93. Method 2: First 3-digit number divisible by 6 is 102 and the last 3-digit number divisible by 6 is 996. Back to the game. So, 42 is divisible by 2. Number of To find three-digit numbers divisible by 6, we need to find the first and last three-digit multiples of 6. Follow answered Jun 10, 2016 at 6:25. Since the sum The number of three digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is 48. 5. Q10. To see if a number is divisible by 3, add the individual digits of the number to each other and see if that number is divisible by 3. is an even number) and 3 (to your point, i. ⇒ 999 ÷ 60. of (6, 7, 8) = 168. Hence, 998 is not divisible by 3. and we know the rules of divisibility by 3. The number of a three-digit number that is divisible by 6 is 150. Therefore, the sum of the digits of the smallest 6-digit number divisible by 18, 24, and 25 is 9. Kamal gets 3 marks for each correctly done question but loses 2 marks for each wrongly done question. Here, 9 + 9 + 6 = 24 is multiple of 3. 151 When checking if a number is divisible by 3, the easiest way to check this is to sum up the digits in 6 and if that resulting number is divisible by 3, then 6 is too. a n = a + (n A number is divisible by 6 if the number is divisible by both 2 and 3. 0. Q. 9k points) A number is divisible by 2 if the last digit is even i. Then, we find the last two-digit number divisible by 3, which is 99. Find the sum of (i) the first 15 multiples of 8 (ii) the first 40 positive integers divisible by (a) 3 (b) 5 (c) 6. Q5. Therefore, a 3-digit number is divisible by 6 if its units and tens digits add up to an even number and the number is divisible by 3. Greatest three-digit number = 999. ⇒ If k = 4, 16 + 2k is divisible by 3. So, the smallest three-digit number divisible by 6 is 102, which is the next multiple of 6. 900 6 = 150, hence, there will be 150 positive three-digit numbers (integers) divisible by 6. If it gives a remainder 2 when divided by 3, then the last digit must be 1, 4 or 7. 166 c. The number is divisible by 6 if it is divisible by both 2 and 3. First three-digit multiple of 6: @$\begin{align*}6 \times 17 = 102\end{align*}@$ Last three 1 Determine the least common multiple (LCM) of 3 and 6, which is 6. To find the largest three-digit number divisible by 6, we need to divide 999 by 6. if the sum of the digits is divisible by 3), then the number is also divisible by 6. Hence the smallest integer multiplier of 30 that produces a 3-digit product is 4, and the smallest 3-digit integer divisible by 30 is 120. Step 2: Determine the smallest three-digit number divisible by 6 To find the smallest three-digit number that is divisible by 6, we can divide 100 by 6 and round up to Answer: When we multiply 24 with 2, 3, 4 we get only 2 digits. What is the largest three digit number divisible by 8? The largest or greatest 3-digit number divisible by 8 is the last number on the list above (last 3 digit number divisible by 8). Long division, remainders, 6-digit by 3-digit. , 996 This is an A. This means that any number that is divisible by both 3 and 6 must also be divisible by 6 To get the sum of 3 digit numbers divisible by 6, first we have to find the first and last 3 digit numbers divisible by 6. This expression can be factored as (A*10 + B) (10101) and the last number is divisible by 37, so ABABAB must be too. Number of numbers divisible by 6 from 100 to 999 : = 166 - 16 = 150. For example, let us consider a random number 468. Total number of such numbers are?: $(1)312$ $(2)3125$ $(3)120$ $(4)216$ My answer is coming out to be $504$. Search Instant Tutoring Private Courses Explore All whole numbers are divisible by 1. Let’s check first if it is divisible by 2. JEE Main 2025 Test Series This is followed by division with the largest three-digit number and addition of the remainder. It is an even number, so it is divisible by 2. Now we get the three digit number 120. 381 (3+8+1=12, and 12÷3 = 4) Yes. The number k53206k would be divisible by 3, if the sum of the digits is divisible by 3. Adding 2 gives the first three digit number divisible by 6 which is 102. Hence, we can conclude that if the sum of digits of a number is divisible by 3 or a multiple of 3, the number is divisible by 3. Assertion :Total number of five-digit numbers having all different digits and divisible by 4 can be formed using the digits {1, 3, 2, 6, 8, 9} is 192. SSC MTS Previous Paper 20 (Held On: 13 August 2019 Shift 2) L. Please help. She just got 495: the last digit is 5. com. A number is divisible by 4 if the last two digits of the number are divisible by 4. Concept used: If any number N is divisible by a set of numbers a, b, c then the L. P with a = 102 , d = 3 , a n = 999 I suppose that you use the rule 'abc is divisible by 3 if a+b+c is divisible by 3', so, if you have same question for 1,2,3,4,5,6,7, you will say that 1,4 and 7 are equivalent, 2 and 5 are equivalent, and 3 and 6 are equivalent. We have to find the number of numbers which are divisible by 6 from 100 to 999. is 15 and the sum of the squares of the extreme terms is 58. What is the largest three digit number divisible by 23? The Three Digit Numbers Divisible By Calculator can calculate all the three digit numbers that can be divided by a number. The 6 digit number is ABABAB in base 10 representation. 999 - 99). How many three digit numbers are divisible by $$6$$? A. The largest 5 digit number is 99996 (6 less). A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, 8). permutations; ⇒ The number should be an even number and sum of its digits should be divisible by 3. Since To find the smallest 3-digit number possible we have to look for smallest 3-digit multiples of 24. What is the largest three digit number divisible by 12? We have 0 + 2 + 3 + 4 + 6 = 15. All even numbers are divisible by 2. Method 1: There are 900 three-digit positive integers (starting at 100 and up to 999, i. C 91. Divisible by 3: A number is divisible by For example: 42 is an even number We know the rules of divisibility by 2. If we subtract 3 from 999, we get the last three digit The three digit numbers divisible by 6 are 102, 108, 114,. divisible by 6 is 12 and the last two digit no. an = a1 + (n-1)*d So for just for 5: 995 = 100 + (n-1)*5 n = 180 And just for 6: 996 = 102 + (n-1)*6 n = 150 The number k53206k would be divisible by 2 if k is an even number i. Example 1: Is the number 255 divisible by 6? Solution: For the number 255 to be divisible by 6, it must divisible by 2 and 3. How can I count the number of numbers divisible by both 5 and 6? For example let's take only tree-digit numbers, how many of them are divisible by both 5 and 6? I know how to do it just for 5 or just for 6, using the arithmetic sequence. Out of the 150000 6-digit numbers divisible by 6, 150000 are even numbers and 0 are odd numbers. a n = a + (n A number is divisible by 3 if the sum of its digits is divisible by 3. 6 from 49 7 from 49; 3 digit 4 digit; 5 digit 6 digit; Magical Random Numbers; Random numbers that SUM up to a specific value; Random numbers whose DIGITS SUM up to a specific value; Random numbers DIVISIBLE by a specific number; Number Lists - all numbers in sequence; More Lists - all numbers; All Permutations and Combinations; receiptLottery The largest three digit number that is exactly divisible by 6, 7 and 8 is: This question was previously asked in. For number to be divisible by ‘6’ unit digit How many 3 digit numbers are divisible by 6 in all ? Answer : The smallest three digit number is 100 and the largest three digit number is 999. Divisibility by 5: The number should have \(0\) or \(5\) as the units digit. 1 5 1. (iii) all 3 − digit natural numbers which are divisible by 13. Step-by-step explanation: To find : What are the largest 4 digit and smallest 3 digit numbers divisible by 6,15,21 & 24 ? Solution : First we find the LCM of the numbers 6,15,21 & 24.
gsyp gsvrfra qmrsl cowrgvle unacp qumjeio psaief ljdcjz dkig enmzotk