# Divisibility Rules Examples and Questions

Examples and detailed solutions on the divisibility of whole numbers are presented. Questions and their solutions are also included.

## Definition of Divisbility

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 Tests

Given a whole number, what test is needed to find out if it is divisible by another number such as 2, 3, ...?### Divisible by 2

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.

### Divisible by 3

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.

### Divisible by 4

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.

### Divisible by 5

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.

### Divisible by 6

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.

### Divisible by 8

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.

### Divisible by 9

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.

### Divisible by 10

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.

## Questions

( with solutions )
Part A

Which of the following numbers are divisible by 2?

a) 4 b) 5 c) 100 d) 408 e) 777 f) 52340 g) 8879

Part B

Which of the following numbers are divisible by 3?

a) 33 b) 53 c) 105 d) 5554 e) 777 f) 9222321

Part C

Which of the following numbers are divisible by 4?

a) 100 b) 3005 c) 12940 d) 5554 e) 7777 f) 9222352

Part D

Which of the following numbers are divisible by 5?

a) 60 b) 362 c) 12940 d) 50016505

Part E

Which of the following numbers are divisible by 6?

a) 120 b) 648 c) 12941 d) 309948

Part F

Which of the following numbers are divisible by 8?

a) 160 b) 11048 c) 12941 d) 10056720

Part G

Which of the following numbers are divisible by 9?

a) 109 b) 10233 c) 12941 d) 1946700

Part H

Which of the following numbers are divisible by 10?

a) 100 b) 3005 c) 12940

## Solutions to the Above Questions

Part A

The following numbers are divisible by 2.

a) 4 c) 100 d) 408 f) 52340

Part B

The following numbers are divisible by 3.

a) 33 c) 105 e) 777 f) 9222321

Part C

The following numbers are divisible by 4.

a) 100 c) 12940 f) 9222352

Part D

The following numbers are divisible by 5.

a) 60 c) 12940 d) 50016505

Part E

The following numbers are divisible by 6.

a) 120 b) 648 d) 309948

Part F

The following numbers are divisible by 8.

a) 160 b) 11048 d) 10056720

Part G

The following numbers are divisible by 9.

b) 10233 d) 1946700

Part H

The following numbers are divisible by 10.

a) 100 c) 12940

## More References and Links

Divisibility CalculatorDivisibility Questions with Solutions

numbers and Fractions.