# Multiples, factors and primes

**Multiples**

A **multiple** of a number is found by multiplying the number by any whole number.

**What are the first six multiples of 6?**

To find the first six multiples of 6 multiply 6 by 1, 2, 3, 4, 5 and 6 to get:

6, 12, 18, 24, 36 and 42

Therefore, any given number can have infinitely many multiples. One way of checking if a number is a multiple of another number is by using divisibility tests.

**Factors**

A **factor** (also known as a divisor) of a number is a whole number that can divide exactly into it.

Factors come in pairs and is explained below:

**What are the factors of 20?**

1 and 20, 2 and 10, 4 and 5.

So, in order, the factors of 30 are:

1, 2, 4, 5, 10 and 20.

Points to note:

- A number will have an odd number of factors when a number is multiplied by itself and the factor pairs are repeated.
- If a number has an odd number of factors, it must be a square number.

**Prime numbers**

**P****rime numbers **are whole numbers with only two factors (1 and the number itself).

For example, the number 19 has only two factors, 1 and 19.

Therefore, 19 is a prime number.

The number 1 has only one factor, 1 and so is not a prime number.

Also, 2 is the only even prime number.