Divisibility Rule

Can you tell whether 3247 is divisible by 2, 3, 4, …, 9 without dividing?

To do that you must know the divisibility rules of various numbers, but today we will see a few.

Divisibility rule of 2

If a number’s last digit is divisible by 2, then the whole number is divisible by 2 (OR) we can say that any even number is divisible by 2.

Example:

14362 is divisible by 2 because 114362 has 2 at the end, 2 is divisible by 2 so 14362 is also divisible by 2.

Divisibility rule of 3 & 9

To find weather a number is divisible by 3 OR 9, you must add all the digits of the number and find the sum. If the sum is divisible by 3 OR 9 then the number is also divisible by 3 OR 9.

Example:

To find if the number 120976 is divisible by 3 then add the digits.
1+2+0+9+7+6= 25, since 25 is not divisible by 3 then “120976” is also not divisible by 3.
To find if the number 12951 is divisible by 9 then add the digits.
1+2+9+5+1= 18 is divisible by 9, so the number is also divisible by 9.

Divisibility rule of 4

If a number’s last 2 digits are divisible by 4 then the whole number is divisible by 4.

Example:

12340, since the last digits of 12340 is divisible by 4 then “12340” is also divisible by 4.

Divisibility rule of 5

If the last digit of a number is 0 or 5 then the number is also divisible by 5.

Example:

457660, the last digit of 457660 is 0 so the number is also divisible by 5.

Divisibility rule of 6

If the number is divisible by 2 and 3 then the number is also divisible by 6.

Example:

To check the number 10932 is divisible by 6, do the following steps,

a. 10932 the last digit is 2, so it is divisible by 2.
b. The sum of 1+0+9+3+2 is 15, which is divisible by 3 so the number is also divisible by 3.
c. From the above statement we found that the number 10932 is divisible by 2 & 3, so it is also divisible by 6.

Divisibility rule of 8

If last 3 digits of the number is divisible by 8 then the number is also divisible by 8.

Example:

2986344, the last 3 digits “344” which is divisible by 8 so the number 2986344 is also divisible by 8.

Divisibility rule of 12

If the number is divisible by 3 and 4 then the number is also divisible by 12.

Example:

To check the number 10932 is divisible by 12, do the following steps,

a. 10932 the last two digits are 32, so it is divisible by 4.
b. The sum of 1+0+9+3+2 is 15, which is divisible by 3 so the number 10932 is also divisible by 3.
c. From the above statement we found that the number 10932 is divisible by 3 & 4, so it is also divisible by 12.

Divisibility rule for number 7, 11 & 13 are little complicated. I will define them in another article. I would prefer not to follow the rules instead I will directly divide the numbers.