Which of the following numbers is divisible by 3, 7, 9 and 11?

Divisibility Rule of 3 The divisibility rule of 3 helps to check whether the given number is divisible by three or not. For small numbers, we can easily conclude the divisibility by 3. In the case of larger numbers, it is not possible to check the divisibility just by looking at the numbers. Thus, we require a specific rule that can be employed for all the numbers to check for the divisibility by 3. In this article, you will learn the divisibility rule of 3, along with solved examples. Learn: What is the Divisibility Rule of 3? The divisibility rule of 3 states that if the sum of digits of a number is a multiple of 3, the number will be completely divisible by 3. Click here to learn what Proof of Divisibility Rule of 3 We can prove the divisibility rule of 3 with the help of an example. Consider the number 4368. Let us expand this number as given below: 4368 = 4 × 1000 + 3 × 100 + 6 × 10 + 8 × 1 = 4 × (999 + 1) + 3 × (99 + 1) + 6 × (9 + 1) + 8 × 1 = (4 × 999 + 3 × 99 + 6 × 9) + (4 × 1 + 3 × 1 + 6 × 1 + 8 × 1) = (4 × 999 + 3 × 99 + 6 × 9) + (4 + 3 + 6 + 8) We know that 9, 99, 999,… are divisible by 3, and thus the multiples of these numbers are also divisible by 3. So, the divisibility of 4368 is now dependent on the sum 4 + 3 + 6 + 8. Here, 4, 3, 6 and 8 are the digits of the number 4368. From the above, we can say that if the sum of these digits is divisible by 3 or a multiple of 3, the number 4368 is divisible by 3. Hence, we can conclude that if the su...

Solution(By Examveda Team) Clearly, 639 is not divisible by 7 Consider 2079 Sum of its digits = (2 + 0 + 7 + 9) = 18 So, it is divisible by both 3 and 9 Also, (79 - 2) = 77, which is divisible by 7 So, 2079 is divisible by 7 Also, (9 + 0) - (7 + 2) = 0 So, 2079 is divisible by 11 Hence, 2079 is divisible by each one of 3, 7, 9 and 11

DivisibilityRules:2, 3, 4, 5, 6, 9, and 10 A number [latex]a[/latex] is divisible by the number [latex]b[/latex] if [latex]a \div b[/latex] has a remainder of zero ([latex]0[/latex]). For example, 15 divided by 3 is exactly 5 which implies that its remainder is zero. We then say that 15 is divisible by 3. In our other lesson, we discussed the 2, 3, 4, 5, 6, 9, and 10. Believe me, you will be able to learn them very quickly because you may not know that you already have a basic and intuitive understanding of it. For instance, it is obvious that all even numbers are divisible by 2. That is pretty much the divisibility rule for 2. The goal of this divisibility rules lesson is to formalize what you already know. Divisibility rules help us to determine if a number is divisible by another without going through the actual division process such as the long division method. If the numbers in question are numerically small enough, we may not need to use the rules to test for divisibility. However, fornumbers whose values are large enough, we want to have some rules to serve as “shortcuts” to help us figure out if they are indeed divisible by each other. A number is divisible by2if the last digit of the number is 0, 2, 4, 6, or 8. Example 1: Is the number 246 divisible by 2? Solution: Since the last digit of the number 246 ends in 6, that means it is divisible by 2. Example 2: Which of the numbers 100, 514, 309, and 768 are divisible by 2? Solution: If we examine all four numbers, on...

A positive integer \(N\) is divisible by • \(\color\] Now we can see that we are left with \(63,\) which we can easily identify as a multiple of 7. Hence 65973390 is a multiple of 7 also. Since 65973390 is divisible by all of 2, 3, 5, 7, it is divisible by \(2\times3\times5\times7=210. \ _\square\) Try some problems for yourself to see if you understand this topic: A positive integer \(N\) is divisible by • \(\color\). Therefore, \(45238\) is not divisible by \(13\). \(_\square\) Is \(2853598728\) divisible by \(24?\) \(24\) is a composite number, so we will have to deal with it in a slightly different way. We can write \(24\) as \( 3 \times 8 \). If a number is divisible by both \(3\) and \(8\), then the number is also divisible by \(24\). We choose \(3\) and \(8\) because they are coprime, and also because we know the divisibility rules for \(3\) and \(8\). Let's test if \(2853598728\) is divisible by \(8\). The last three digits of the number are \(728\) which is divisible by \(8\), so \(2853598728\) is also divisible by \(8\). Now let's see if \(2853598728\) is divisible by \(3\). The sum of digits of \(2853598728\) is \(57\). Since \(57\) is divisible by \(3\), \(2853598728\) is also divisible by \(3\). Since \(2853598728\) is divisible by both \(3\) and \(8\), we can conclude that \(2853598728\) is divisible by \(24\). \(_\square \) Is \(365226929\) divisible by \(2976?\) We do not know the divisibility rule for \(2976\). However, we know that since \(2976\) is even,...

Lessons with videos, examples, solutions and stories to help Grade 4 students learn the Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13. The following table gives the Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Scroll down the page for examples and solutions. Divisibility means one number divides into another number and there is not a remainder. Divisibility Tests For 2, 3, 5, 7 And 11 This shows you the divisibility tests for 2, 3, 5, 7, and 11, so you can tell if those numbers are factors of a given number or not without dividing. • Divisibility Test for 2: The last digit is 0, 2, 4, 6, or 8. • Divisibility Test for 3: The sum of the digits is divisible by 3. • Divisibility Test for 5: The last digit is 0 or 5. • Divisibility Test for 7: Cross off last digit, double it and subtract. Repeat if you want. If new number is divisible by 7, the original number is divisible by 7. • Divisibility Test for 11: For a 3-digit number, sum of the outside digits minus the middle digit must be 0 or 11. • Divisible by 2: A number is divisible by 2 if the last digit is even i.e. 0, 2, 4, 6, or 8. Example: 138 is divisible by 2 because the last digit, 8, is even. 249 is not divisible by 2 because the last digit, 9, is not even. Divisible by 3: A number is divisible by 3 if the sum of the digits is divisible by 3. 372 is divisible by 3 because 3+7+2 = 12 and 12 ÷ 3 = 4. 218 is not divisible by 3 because 2+1+8 = 11 and 11 ÷ 3 = 3 2/3. Divisible by 4: A num...