# Whole Numbers: Factors and Multiples

### Factors

Example
Let's find the factors of 8.

1 × 8 = 8
8 is the product of 1 and 8.
So 1 and 8 are factors of 8.

2 × 4 = 8
8 is the product of 2 and 4.
So 2 and 4 are factors of 8.
1 is a factor of every number.
Every number is a factor of itself.

The factors of 8 are 1, 2, 4 and 8.

### Multiples

Example
Let's find the multiples of 8.

To find the multiple of 8, think of the times table of 8 as below.

 8 × 1 = 8, 8 × 2 = 16, 8 × 3 = 24, 8 × 4 = 32, 8 × 5 = 40, 8 × 6 = 48,

8 is a factor of all the multiples of 8.
8, 16, 24, 32, 40 and 48 are multiples of 8.

### Problem 1

List all the factors of 60.
60 = 1 × 60
60 = 2 × 30
60 = 3 × 20
60 = 4 × 15
60 = 5 × 12
60 = 6 × 10

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.

### Problem 2

What are the common factors of 16 and 24? What is the greatest common factor of 16 and 24?
The factors of 16 are: 1, 2, 4, 8 and 16.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24.

The common factors of 16 and 24 are 1, 2, 4 and 8.

The greatest common factor (GCF) of 16 and 24 is 8.

### Problem 3

List the first five multiples of 6. What is the twelfth multiple of 6?
 6 × 1 = 6, 6 × 2 = 12, 6 × 3 = 18, 6 × 4 = 24, 6 × 5 = 30, 6 × 6 = 36,

The first multiple of 6 is 6.

The second multiple of 6 is 12.

The third multiple of 6 is 18.

The fourth multiple of 6 is 24.

The fifth multiple of 6 is 30.

The sixth multiple of 6 is 36.

6 × 12 = 72
The twelfth multiple of 6 is 72.

### Problem 4

Is 21 a multiple of 7?

21 can be divided exactly by 7.
21 is a multiple of 7.
7 is a factor of 21.

### Problem 5

Is 25 a multiple of 7?

25 cannot be divided exactly by 7.
25 is not a multiple of 7.
7 is not a factor of 25.

### Problem 6

Find the first six multiples of 2 and 5. What is a common multiple of 2 and 5?
The first six multiples of 2 are 2, 4, 6, 8, 10 and 12.

The first six multiples of 5 are 5, 10, 15, 20, 25 and 30.

A common multiple of 2 and 5 is 10.

### Problem 7

I'm thinking of a one-digit number, N, which is greater than 1. N and 7 are the common factors of 14 and 28. What is the number I'm thinking of?
The factors of 14 are 1, 2, 7 and 14.
The factors of 28 are 1, 2, 4, 7, 14 and 28.

The common factors of 14 and 28 are 1, 2, 7 and 14.
The one-digit common factor of 14 and 28 other than 1 and 7 is 2.

N is 2.