Number System Divisibility Rules

 Divisibility rules in math are a set of specific rules that apply to a number to check whether the given number is divisible by a particular number or not. Some known divisibility tests are for numbers 2 to 20. It helps us to find the factors and multiples of numbers without performing long division. A person can mentally check whether a number is divisible by another number or not by applying divisibility rules. Let us learn more about divisibility tests in this article.

 

Divisible by 2:

A number which 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:

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. A number which is even or a number whose last digit is an even number i.e. 0, 2, 4, 6, and 8; and The sum of all the digits of the number should be divisible by 3.

 

Divisible by 7:

Subtracting 2 times the last digit of the number from the remaining digits gives a multiple of 7.

 

Divisible by 8:

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.

 

Divisible by 13:

Multiply the unit place digit by 4, and add the product with the rest of the number to the left of the unit place digit. If the resulting number is a 0 or multiples of 13, then the number is divisible by 13.

For example, in the number 416, the ones place digit is 6. Multiplying the ones place digit by 4, we get (4 x 6), which is 24. Adding 24 to the rest of the digits to the left, we get 41 + 24 = 65. Since 65 is a multiple of 13, 416 is divisible by 13.

 

Divisible by 14:

It is divisible by 2 and by 7.

 

 Divisible by 15:

 It is divisible by 3 and by 5.

 

 Divisible by 16:

A number is divisible by 16 if the thousands digit is even and the last three digits form a number that is divisible by 16. A number is also divisible by 16 if the thousands digit is odd and the number formed by the last three digits plus 8 is divisible by 16.

For example, in 654,320, the thousands digit (4) is even and the last three digits form 320 which is divisible by 16. Thus, 654,320 is divisible by 16.

Now let us take, 123,457. In this case, the thousands digit (3) is odd, so then we take the last 2 digits and add 8: 57 + 8 = 65. 65 is not divisible by 16, thus 123,457 is not divisible by 16.

 

 Divisible by 17:

A number is divisible by 17 if you multiply the last digit by 5 and subtract that from the rest. If that result is divisible by 17, then your number is divisible by 17.

For example, for 986, you do: 98 - (6 x 5) = 68. Since, 68 is divisible by 17, then 986 is also divisible by 17.

However, 876 is not divisible by 17 because 87 - (6 x 5) = 57 and 57 is not divisible by 17.

 

 

Divisible by 18:

A number is divisible by 18 if it is an even number AND the sum of its digits is divisible by 9.

For example, 492,480 is divisible by 18 because it is an even number and the sum of its digits is 4 + 9 + 2 + 4 + 8 + 0 = 27 is divisible by 9.

However, 246,802 is not divisible by 18 because although it is an even number, the sum of its digits is 2 + 4 + 6 + 8 + 0 + 2 = 22 is not divisible by 9.  

Divisible by 19:

 To determine if a number is divisible by 19, take the last digit and multiply it by 2. Then add that to the rest of the number. If the result is divisible by 19, then the number is divisible by 19.

For example, 475 is divisible by 19 because 47 + (5 x 2) = 57, and 57 is divisible by 19.

 

 Divisible by 20:

A number is divisible by 20 if the tens digit is an even number AND the ones digit is 0.

For example, 246,260 is divisible by 20 because the tens digit (6) is even and the ones digit is 0.

However, 246,269 is not divisible by 20 because although the tens digit (6) is even, the ones digit (9) is not a 0.

Remember, both conditions must be met for the number to be divisible by 20.