Tutorials with problems and detailed solutions on the divisibility of whole numbers are presented. Exercies are also included at the bottom of the page.

Definition.

A whole number n is divisible by another number m if the division n / m yields a remainder equal to 0. m is called the factor of n.

Example: 15 is divisible by 5 because 15 / 5 = 3 and remainder is equal to 0. Also 15 = 3 * 5. Both 3 and 5 are factors of 15. Also 15 / 3 = 5. 15 is also divisible by 3.

Divisibilty Test.

1. If the last digit in a whole number is 0, 2, 4, 6 or 8, then that whole number is divisible by 2.

Example: 23464568 is divisible by 2 since the last digit is 8.

2. If the sum of the digits of a whole number is divisible by 3, then that whole number is divisible by 3 .

Example: 1272 is divisible by 3 since 1+2+7+2 = 12 is divisible by 3.

3. If the number formed by the last two digits of a whole number is divisible by 4, then that whole number is divisible by 4.

Example: 1869520 is divisible by 4 since 20 (last two digits) is divisible by 4.

4. If the last digit of a whole number is either 0 or 5, then that whole number is divisible by 5.

Example: 52745 is divisible by 5 since the last digit is 5.

5. If a whole number is divisible by 2 and divisible by 3, then that whole number is divisible by 6.

Example: 1890 is divisible by 2 (last digit 0) and divisible by 3 (1+8+9+0 = 18). 1890 is divisible by 6.

6. If the number formed by the last three digits of a whole number is divisible by 8, then that whole number is divisible by 8.

Example: 18567160 is divisible by 8 since 160 (last 3 digits) is divisible by 8.

7. If the sum of the digits of a whole number is divisible by 9, then that whole number is divisible by 9.

Example: 1006506 is divisible by 9 since 1+0+0+6+5+0+6 = 18 is divisible by 9.

8. If the last digit of a whole number is 0, then that whole number is divisible by 10.

Example: 12635360 is divisible by 10 since the last digit is 0.