Divisibility Rules

Is 841 divisible by 3?

Add the digits 8, 4, and 1 to test. 8 + 4 + 1 = 13. 13 is not divisible by 3

Is 8,568 divisible by 9 and 8?

Add the digits to test if it is divisible by 9. 8 + 5 + 8 + 8 = 27. 27 is divisible by 9. Take the last three digits to test if it is divisible by 8. 568 / 8 = 71, no remainder. 8.568 is divisible by 8 and 9.

A number is divisible by 10

If the number ends in 0

A number is divisible by 5

If the number ends in 0 or 5

A number is divisible by 6

If the number is divisible by 2 and 3

A number is divisible by 9

If the sum of the digits is divisible by 9

Which of these numbers {2, 3, 4, 5, 6, 8, 9, 10} is 180 divisible by?

180 ends in 0, so it is divisible by 2, 5, and 10. The sum of the digits 1 + 8 + 0 = 9, so it is divisible by 3 and 9. 180 is a multiple of 6 because it is divisible by 2 and 3. The last two digits is 80, and 80 is divisible by 4, so 180 is divisible by 4. The last three digits of 180 are 180 and 180 / 8 = 22, remainder 4. 180 is not divisible by 8. So 180 is divisible by 2, 3, 4, 5, 6, 8, and 10.

Is 142,637 divisible by 11?

To test divisibility by 11, add up the even-numbered digits and the 0dd-numbered digits. The even-numbered digits are 1, 2, 3 and the odd-numbered digits are 4, 6, 7. 1 + 2 + 3 = 6, and 4 + 6 + 7 = 17. The positive difference of these two numbers is 11. 142,637 is divisible by 11.

A number is divisible by 11

if the difference between the sum of the even-numbered digits and the sum of the odd-numbered digits is 0 or a multiple of 11

A number is divisible by 8

if the last three digits make a three-digit number that is divisible by 8

A number is divisible by 4

if the last two digits make a two-digit number that is divisible by 4

A number is divisible by 12

if the number is divisible by 3 and 4

General divisibility rule for an integer N, where N = p * q

if the number is divisible by p * q. For example: the divisibility rule for the number 6

A number is divisible by 2

if the number is even or ends in 0, 2, 4, 6, or 8

A number is divisible by 3

if the sum of the digits is divisible by 3

A shortcut to find the remainder when a number is divided by 2, 5, or 10

is to find the sum of the digits and divide it by 2, 5, or 10

A shortcut to find the remainder when a number is divided by 3 or 9

is to find the sum of the digits and divide it by 3 or 9

A shortcut to find the remainder when a number is divided by 8

is to find the three-digits number from the last three digits and divide it by 8

A shortcut to find the remainder when a number is divided by 4

is to find the two-digits number from the last two digits and divide it by 4