Maths How To with Anita

# The Factors of 120 and How to find them

In this article, I discuss the factors of 120. I show you how to find them using various methods, including factor trees, factor rainbows, prime factorization, and a calculator.

Once you understand how to find the factors of 120, you can use that knowledge to find the factors of any number!

## What are the factors of 120?

The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.

They are the numbers that divide exactly into 120 without a remainder.

## How to find the factors of 120

To find the factors of 120, you can use a variety of methods. The easiest way is to use a calculator and divide 120 by every whole number starting with 1. If the answer is a whole number then both numbers are factors. They are a factor pair.

## Factor pairs of 120.

I like to use a combination of my calculator and drawing a factor rainbow to find the factors of 120.

Is that pretty?!!

The factor pairs of 120 are the 2 numbers in the same color in the rainbow.

Factor pairs multiply together to give a product of 120.

1 x 120 =120

2 x 60 = 120

3 x 40 = 120

4 x 30 = 120

5 x 24 = 120

6 x 20 = 120

8 x 15 = 120

10 x 12 = 120

So there are 8 factor pairs of 120.

## Prime factorization of 120

To find the prime factors of 120 it is best to draw a factor tree.

You can draw a factor tree for 120 in many different ways but you will always end up with the same prime factors.

## Factor tree for 120

Here is one factor tree of 120:

Here is another one:

## What are the prime factors of 120?

The prime factors of 120 are 2, 3, & 5.

They are the numbers circled red in the factor trees above.

You can use the prime factors to express 120 as a product of its prime factors, also called the prime factorization of 120.

120 = 2 x 2 x 2 x 3 x 5

This can be written in index notation like this:

## Negative Factors of 120

The negative factors of 120 are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60, -120.

Both factors need to be negative (or both positive) to result in a product of positive 120.

## Final thoughts on the Factors of 120

So there you have it! I have shown you a variety of ways to find the factors of 120. Practice a little with each method and see which one works best for you. And remember, when in doubt, use a calculator!

## Further Factors!

Factors of 18

Factors of 30

Prime Factorization of 42

Factors of 50

Factors of 64

Factors of 90

Factors of 91

Factors of 96

Factors of 120