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Divisibility Rules

Divisibility Rules: Examples, Basic Divisibility Rules, Intermediate Divisibility Rules and Divisibility By Number Table

Have you ever thought of the exact meaning of ‘Divisible By’? Well, in a broader sense, this refers to a process – That, when you divide one number by another, the result is a whole number.

When you say ‘divisible’, it means that when you divide one number by another, the remainder should be zero.

For example, to check if a number is even, implying if it is divisible by 2, you need to check the last digits of the number to see if they are - 2, 4, 6, 8, or 0. Similarly, there are certain ways to check the divisibility for other numbers too.

Divisibility rules allow you to evaluate if a number is divisible by another, without performing long division.

SO, WHAT ARE THESE DIVISIBILITY RULES?

A divisibility rule is a shortcut to find out if a given number is divisible by a particular number, without the use of the whole division process, rather, by just performing a basic test.

There is another advantage to these rules. You can apply multiple divisibility rules to the same number, which would enable you to determine its prime factors.

BASIC DIVISIBILITY RULES

Now, let us look at some of the basic divisibility rules. 

DIVISIBILITY BY NUMBER

DIVISIBILITY RULE

2

If the last digit ends in 2, 4, 6, 8, 0

3

If the sum of the digits equals 3

4

If the last 2 digits is a multiple of 4

5

If the last digit ends in 0 or 5

6

If the number is divisible by both 2 and 3, then it is also divisible by 6 

7

Double the last digit and subtract it from the remaining digits. Now check if it is a multiple of 7

8

If the last three digits are a multiple of 8

9

This is quite similar to 3. Add all the digits and check if it is a multiple of 9

10

If the last digit ends in 0

11

Add the alternate digits and then subtract them, and check if the resulting number is a multiple of 11

12

If the digits are divisible by both 3 and 4

INTERMEDIATE DIVISIBILITY RULES

The basic divisibility rules are quite simple and easier to find out. For certain numbers like 13, 17, and 19, we require more steps to check divisibility. Intermediate divisibility rules apply to prime numbers that lie between 10 and 20.

DIVISIBILITY BY NUMBER

DIVISIBILITY RULE

13

Multiply the last digital by 4 and add this product to the remaining digits. Continue the same process until you get a two-digit number. Now check if the resulting number is a multiple of 13

17

Multiple the last digit by 5 and subtract the resulting product from the remaining digits and check if it is a multiple of 17

19

Double the last digit and add it to the remaining digits and check if it is a multiple of 19

 

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