Divisibility Rules - Examples, Chart, Rules Of Divisibility 1 To 13

Divisibility Rules

Divisibility rules are rules that are applied to a number to check whether the given number is divisible by a particular number or not. These divisibility tests help us skip the process of long division and help us mentally check if a number is completely divisible by another number. Let us learn more about the divisibility test and the divisibility rules with examples in this article.

1.	What are Divisibility Rules?
2.	Divisibility Rules 2 to 12
3.	Divisibility Rules for Prime Numbers
4.	FAQs on Divisibility Rules

What are Divisibility Rules?

A divisibility rule is a kind of shortcut that helps us to identify if a given number is divisible by a divisor by examining its digits, without performing the long division process. These divisibility rules help us determine the actual divisor of a number just by considering the digits of that number. These are also called divisibility tests which help in larger calculations and ease out the process of simplification of numbers.

Divisibility Rules 2 to 12

In this section, let us learn about basic divisibility tests from 2 to 12. The divisibility rule of 1 is not required since every number is divisible by 1.

Divisibility by number	Divisibility Rule
Divisible by 2	A number that is even or a number whose last digit is an even number, i.e., 0, 2, 4, 6, and 8.
Divisible by 3	The sum of all the digits of the number should be divisible by 3.
Divisible by 4	The number formed by the last two digits of the number should be divisible by 4 or should be 00.
Divisible by 5	Numbers having 0 or 5 as their ones place digit.
Divisible by 6	A number that is divisible by both 2 and 3.
Divisible by 7	Subtracting twice the last digit of the number from the remaining digits gives a multiple of 7.
Divisible by 8	The number formed by the last three digits of the number should be divisible by 8 or should be 000.
Divisible by 9	The sum of all the digits of the number should be divisible by 9.
Divisible by 10	Any number whose ones place digit is 0.
Divisible by 11	The difference of the sums of the alternative digits of a number is divisible by 11.
Divisible by 12	A number that is divisible by both 3 and 4.

Divisibility Rules Chart and Examples

Let us try to understand the above divisibility tests with examples.

• Is 280 divisible by 2? Yes, 280 is divisible by 2 as the units place digit is 0.
• Is 345 divisible by 3? Yes, 345 is divisible by 3, as the sum of all the digits, i.e., 3 + 4 + 5 = 12, and 12 is divisible by 3. So, 345 is divisible by 3.
• Is 450 divisible by 4? No, 450 is not divisible by 4 as the number formed by the last two digits starting from the right, i.e., 50 is not divisible by 4.
• Is 3900 divisible by 5? Yes, 3900 is divisible by 5 as the digit at the units place is 0 which satisfies the divisibility rule of 5.
• Is 350 divisible by 6? The sum of all the digits of 350 is 8, so it is not divisible by 3. Hence it cannot be divisible by 6, as a number needs to be a common multiple of both 2 and 3 to be a multiple of 6.
• 357 is divisible by 7 as when we subtract the twice of the ones place digit, 7 × 2 = 14, and subtract it from the remaining digits 35, we get 35 -14 = 21, which is divisible by 7. So, 357 is divisible by 7.
• 79238 is not divisible by 8, as the number formed by the last three digits 238 is not completely divisible by 8.
• 875 is not divisible by 9, as the sum of all the digits, 8 + 7 + 5 = 20 is not divisible by 9.

Now, let us take the number 1000 and see its divisibility by 2 to 10. It is clearly seen in the following figure that 1000 is divisible by 2, 4, 5, 8, and 10, and not divisible by 3, 6, 7, and 9. We find this by applying the divisibility rules of 2 to 10, and not by performing division which can be more time-consuming.

Divisibility Rules for Prime Numbers

Intermediate divisibility rules are applied to prime numbers which are less than 20 and greater than 10. Divisibility tests for prime numbers 2, 3, 5, 7, and 11 are already discussed above. Here, let's learn about the divisibility rules of 13, 17, and 19.

Divisibility Rule of 13 - A number is divisible by 13 if it leaves 0 as the remainder when we divide it by 13. The divisibility test of 13 helps us quickly know if a number is divisible by 13 or not without performing long division. According to the divisibility rule of 13, first, we need to multiply the ones place digit by 4. Then, we add the product to the rest of the number to its left (excluding the digit at the units place). If that sum results in a number divisible by 13, then the original number is also divisible by 13. Apart from this method, there are three other divisibility rules of 13 that are explained in this article - Divisibility Rule of 13.

Divisibility Rule of 17 - A number is divisible by 17 when 17 divides it completely without leaving any non-zero remainder. According to the divisibility rule of 17, first, we need to multiply the ones place digit by 5. Then, we subtract the product from the rest of the number to its left (excluding the digit at the units place). If that difference results in a number divisible by 17, then the original number is also divisible by 17.

Divisibility Rule of 19 - If we get 0 as the remainder when dividing a number by 19, then that number is considered divisible by 19. According to the divisibility rule of 19, first, we need to multiply the ones place digit by 2. Then, we add the product to the rest of the number to its left (excluding the digit at the units place). If that sum results in a number divisible by 19, then the original number is also divisible by 19.

Divisibility Rules of 13, 17, and 19 Examples

Let us take the example of number 1326, and check its divisibility by 13, 17, and 19. Observe the figure given below to understand this example.

Divisibility Rules Tips and Tricks:

• Divisibility rules are of great importance while checking prime numbers.
• These are handy to solve word problems.
• They are useful to do quick calculations.
• Every even number is divisible by 2.
• Every leap year is divisible by 4.

Divisibility Tests of Numbers

Also, check these articles related to the divisibility rules.

• Divisibility Rule of 3
• Divisibility Rule of 4
• Divisibility Rule of 5
• Divisibility Rule of 6
• Divisibility Rule of 7
• Divisibility Rule of 8
• Divisibility Rule of 9
• Divisibility Rule of 11