Factors

# Factors of 120 | Prime Factorization of 120 | Factor Tree of 120

Written by Prerit Jain

Updated on: 12 Aug 2023

### Factors of 120 | Prime Factorization of 120 | Factor Tree of 120

The factors of 120 are the numerals that will give 120 after being multiplied. Several factors are common and are used in math calculations, for example, 2, 56, etc.

We can also use the division or prime factorization method to find the factors of a number. Let us understand how to find factors of 120, prime factorization of 120, solved examples, and the factor tree of 120. Scroll down to find out more.

## What Are the Factors of 120?

The 120 factors are the numbers that can be divided by 120 without leaving a remainder. Furthermore, they can also be the numbers that give 120 as a result after being multiplied in pairs. As the number 120 is a composite number, it has several factors, and they are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120, which are the 120 factors.

## Write Factors of 120 in Pairs?

The positive and negative factors of 120 are given below:

### Positive Pairs Factors of 120

The 120 positive pairs are (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12).

### Negative Pair Factors of 120

The 120 negative pairs are (-1, -120), (-2, -60), (-3, -40), (-4, -30), (-5, -24), (-6, -20), (-8, -15), and (-10, -12).

## How to Find Factors of 120 Through Division Method?

You can use the division method to find 120 factors. In this method, you will divide each integer by 120, and if they leave 0 as a remainder, that means they are 120 factors. Let us understand how to use the division method to find 120 factors:

• 120 ÷ 1 = 120
• 120 ÷ 2 = 60
• 120 ÷ 3 = 40
• 120 ÷ 4 = 30
• 120 ÷ 5 = 24
• 120 ÷ 6 = 20
• 120 ÷ 8 = 15
• 120 ÷ 10 = 12
• 120 ÷ 12 = 10
• 120 ÷ 15 = 8
• 120 ÷ 20 = 6
• 120 ÷ 24 = 5
• 120 ÷ 30 = 4
• 120 ÷ 40 = 3
• 120 ÷ 60 = 2
• 120 ÷ 120 = 1

Therefore, we can see that 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 are 120 factors.

## What Is the Prime Factorisation of 120?

As 120 is a composite number, there are more than prime factors. The detailed steps on how to find prime factors of 120 using the prime factorization method are given below:

Step 1: Firstly, we will divide 120 with 2, as it’s the smallest prime number.

• 120 ÷ 2 = 60

Step 2: Now, we will keep dividing the quotient repeatedly with the smallest prime number, until the quotient is the prime number.

• 60 ÷ 2 = 30
• 30 ÷ 2 = 15

Step 3: As we cannot divide 15 by 2, we will choose 3 as it’s the next smallest prime number 15 is divisible by.

• 15 ÷ 3 = 5

Step 4: Since 5 is a prime number, it can only be divided by 1 or 5, so we will divide it by 5.

• 5 ÷ 5 = 1

Hence 1 cannot be divided anymore, we need to round all the prime numbers.

Therefore, 2 X 2 X 2 X 3 X 5 or 23 X 3 X 5 are the prime numbers of 120. Below is an image for better understanding.

## Write the Factor Tree of 120

Students can also use the factor tree to find the 120 prime factors. In a factor tree, we divide a number until the answer becomes 1, and the factors are written in the form of branches of a tree. Then, the last factors are circled, and they are the prime factors of the number. The detailed steps on how to do this are explained below.

• Step 1: Let’s place the number 120 at the top and write down 120 in pairs, that is, 10 and 12.
• Step 2: Since both are composite numbers, we have to separate them.
• Step 3: We will now divide 10 into 2 and 5.12 will be split into 3 and 4.
• Step 4: As we can see, 2, and 5 are prime numbers. We will leave them. But 3 is a prime number and 4 is not, so we will split 4 into 2 and 2.
• Step 5: Now, once again, we will leave 2 as it is because it is a prime number.
• Step 6: We can see that all of them are prime numbers. The branches in the factor tree will now be all the prime numbers.

Circling all the branches, 23 X 3 X 5 or 2 X 2 X 2 X 3 X 5= 120, which are 120 prime factors. Below is an image of what the factor tree of 120 should look like:

There are many ways on which we can devise the factor tree of 48. Below is an image representation of the factor tree of 120, choosing 2 and 60 as pair factors of 120.

## Solved Examples on Factors of 120

Here are some solved examples on 120 factors:

What is the sum of all the factors of 120?
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 are the 120 factors.
1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 + 120 = 360.
Hence, 360 is the sum of all 120 factors.

What are the factors and primefactors of 120?
The 120 factors are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
The 120 prime factors are: 23 X 3 X 5 or 2 X 2 X 2 X 3 X 5.

What’s the highest common factor between 60 and 120?
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Hence, from the above, the common factor of 60 and 120 is 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The highest common factor between 60 and 120 is 60.

What’s the highest common factor between 160 and 120?
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, and 160.
Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
Hence, from the above, the common factor of 160 and 120 is 1, 2, 4, 5, 8, 10, 20, and 40.
The highest common factor between 160 and 120 is 40.

Is 50 a factor of 120?
No, 50 is not a factor of 120.
As 120 ÷ 50 = leaves a remainder.

Is 24 a factor of 120?
Yes, 120 is a factor of 120.
As 120 ÷ 24 = 5.

## FAQs on Factors of 120

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

What are the composite factors of 120?
4, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 are the composite factors of 120. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 120 in pairs?
(1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12) are the 120 pair factors.

What are the positive factors for 120?
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 24, 30, 40, 60 and 120 are the positive factors for 120.

That is all about factors of 120 for today. We hope this has been useful, and that you were able to learn about 120 factors, division method, factor tree, and much more.

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Prerit Jain

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