Divisibility Tests of Whole Numbers

Divisibility Tests of Whole Numbers


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.


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