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 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
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 12
if the number is divisible by 3 and 4
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
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 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.
