Divisibility Rules
Ways to determine if one number can evenly be divided by another, without actually
dividing them.
Number Rule Example Divisible?
2 The last digit is even: 5 7 6 is even YES
(0,2,4,6,8). 8 3 1 is not even NO
5 3 7 --- 5+3+7 = 15, YES
3 The sum of the digits is 15 ÷ 3 = 5
divisible by 3. 8 3 3 --- 8+3+3 = 14,
14 ÷ 3 has a remainder NO
Double the tens digit and 2 5 7 6 --- 2 x 7 + 6 = 20, YES
4 add to the ones digit. 20 ÷ 4 = 5
This answer is divisible 2 5 2 5 --- 2 x 2 + 5 = 9,
by 4. 9 ÷ 4 has a remainder NO
3 8 5 last digit is 5 YES
5 The last digit is 0 or 5. 9 6 4 last digit is 4 NO
4 3 2 --- even; YES
4+3+2 = 9 and 9 ÷ 3 = 3
6 The number is divisible 5 2 4 --- even;
by both 2 and 3. 5+2+4 = 11 and 11 ÷ 3 NO
has a remainder
Double the last digit and 5 8 1 --- 2 x 1 = 2,
subtract it from the 58 - 2 = 56 YES
rest of the number. and 56 ÷ 7 = 8
7 This answer is 0 or
divisible by 7. 3 2 1 --- 2 x 1 = 2
* You can apply this rule 32 - 2 = 30 and 30 ÷ 7 NO
to that answer again. has a remainder
Fall 2017
Ways to determine if one number can evenly be divided by another, without actually
dividing them.
Number Rule Example Divisible?
2 The last digit is even: 5 7 6 is even YES
(0,2,4,6,8). 8 3 1 is not even NO
5 3 7 --- 5+3+7 = 15, YES
3 The sum of the digits is 15 ÷ 3 = 5
divisible by 3. 8 3 3 --- 8+3+3 = 14,
14 ÷ 3 has a remainder NO
Double the tens digit and 2 5 7 6 --- 2 x 7 + 6 = 20, YES
4 add to the ones digit. 20 ÷ 4 = 5
This answer is divisible 2 5 2 5 --- 2 x 2 + 5 = 9,
by 4. 9 ÷ 4 has a remainder NO
3 8 5 last digit is 5 YES
5 The last digit is 0 or 5. 9 6 4 last digit is 4 NO
4 3 2 --- even; YES
4+3+2 = 9 and 9 ÷ 3 = 3
6 The number is divisible 5 2 4 --- even;
by both 2 and 3. 5+2+4 = 11 and 11 ÷ 3 NO
has a remainder
Double the last digit and 5 8 1 --- 2 x 1 = 2,
subtract it from the 58 - 2 = 56 YES
rest of the number. and 56 ÷ 7 = 8
7 This answer is 0 or
divisible by 7. 3 2 1 --- 2 x 1 = 2
* You can apply this rule 32 - 2 = 30 and 30 ÷ 7 NO
to that answer again. has a remainder
Fall 2017
