Hello. This page is about number factors.

**Table Of Contents**

**What Is A Factor?**

A factor is a positive whole number which (exactly) divides into a whole number with a zero remainder. In other words, a whole number divided by a factor gives another whole number exactly. As an example, any even number can be divided by 2 with zero remainder.

**Examples of Number Factors**

Here are some examples.

The number 6 has factors of 1, 2, 3 and 6 itself. These factors divide into 6 exactly since , , , and .

The number 20 has factors of 1, 2, 4, 5, 10 and 20 itself. We can have , and . Alternatively, we can show that , , , , and , and .

We look at an interesting case. The number 7 has factors of just 1 and 7 itself. Because 7 has two factors which are 1 and itself, the number 7 is an example of a prime number. Other prime numbers include 3, 5, 11, 13, 17 and 19.

Factors are not restricted to numbers. We can use variables such as . As an example, factors of are 1, and itself.

**Practice Problems**

**1)** What are the factors of the number 12?

**2)** What are the factors of the number 49?

**3)** What are the factors of the number 25?

**4)** Is 31 a prime number? Why?

**5)** What are the factors of ?

**6)** What are the factors of ?

**Answers**

**1)** 1, 2, 3, 4, 6 and 12

**2)** 1, 7, 49

**3)** 1, 5, 25

**4)** The factors of 31 are 1, and 31 itself. It is a prime number.

**5)** Factors of are 1, , , and itself.

**6)** Factors of include 1, 2, , and .