# 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