Divisibility Rules printable pdf download

Divisibility Rules

An integer N is evenly divisible by

if the last digit is even (0, 2, 4, 6, or 8);

Example: 123,456 is divisible by 2, because the last digit, 6, is even.

if the sum of its digits is divisible by 3;

Example: 123,456 is divisible by 3, because 1 + 2 + 3 + 4 + 5 + 6 = 21, which is divisible by 3. (21

÷ 3 = 7)

if the number formed by the two last digits is divisible by 4;

Example: 123,456 is divisible by 4, because 56 is divisible by 4.

(56 ÷ 4 = 14)

if it ends in 5 or 0;

Examples:

123,456 is not divisible by 5, because the last digit, 6, is not 0 or 5.

12,345 is divisible by 5, because the last digit is 5.

if it is divisible by both 2 and 3;

Example: 123,456 is divisible by 6, since it is divisible by both 2 and 3. (See examples for 2 and

3 above.)

if the number formed after the following two steps is divisible by 7:

 First, remove the last digit,

 Then, from the number remaining, subtract two times the digit we just removed;

See examples on the back of this page.

if the number formed by the last three digits is divisible by 8;

Example: 123,456 is divisible by 8, because 456 is divisible by 8.

(456 ÷ 8 = 57)

if the sum of its digits is divisible by 9;

Examples:

123,456 is not divisible by 9, since 1 + 2 + 3 + 4 + 5 + 6 = 21 is not divisible by 9.

123,453 is divisible by 9, since 1 + 2 + 3 + 4 + 5 + 3 = 18 is divisible by 9. (18 ÷ 9 = 2)

if it ends in 0;

Examples:

123,456 is not divisible by 10, since its last digit, 6, is not 0.

123,450 is divisible by 10, since its last digit is 0.

for two-digit numbers, if it is double,

Examples: 11, 22, 33, 44, 55, 66, 77, 88, and 99 are each divisible by 11.

for larger numbers, if the number formed after the following three steps is divisible by 11:

 find the sum of alternate digits,

 find the sum of the remaining digits,

 find the difference of these two sums;

See examples on the back of this page.

if it is divisible by both 3 and 4.

Example: 123,456 is divisible by 12, since it is divisible by both 3 and 4.

(See examples for 3 and 4 above.)

Divisibility Rules