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!
