# Factors of 120

## Prime Factorization of 120

The factors of 120 are all the numbers that give the result as the number 120 when they are multiplied together in a pair of two. There are many different factors that are commonly used in the mathematical calculations, for example, the factors of the numbers 56, 90, etc. The prime factors of the number 120 basically give you the prime numbers. For finding the factors of the number 120, you need to use the multiplication method. The multiplication method gives you the prime factorization of 120 and hence, you will get all the factors of the number. In this article, we will learn in detail about what are the factors of 120, what is the prime factorization of 120, and the prime factorization of 120 using a factor tree.

### Factor Pairs of 120

The factor pairs of 120 refers to all the different combinations of the two factors of 120 which you multiply together to get the answer as 120. It is a two-step process for creating all the factor pairs of 120. First, you need to list all the factors of 120. Then, you need to pair all the different combinations of these factors and it will give you all the factor pairs of 120.

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

All of the different pair combinations from these factors of 120 are called the factor pairs of 120. Given below is the list of all the factor pairs of 120. As you can see, all the factor pairs of 120 equal to the number 120 if you multiply them together.

• 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

• 12 x 10 = 120

• 15 x 8 = 120

• 20 x 6 = 120

• 24 x 5 = 120

• 30 x 4 = 120

• 40 x 3 = 120

• 60 x 2 = 120

• 120 x 1 = 120

The factors of 120 include the negative numbers as well since minus times minus results to plus. Hence you can convert all the positive factor pairs simply putting a minus sign in front of each factor and you will get all the negative factor pairs of 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 = 120

### Prime Factorization of 120

Let us now learn about the prime factorization of 120 using a factor tree.

120 is a composite number. Hence, its prime factorization is as follows:

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1. The first step is dividing the number 120 with the smallest prime factor which is 2 and continue dividing the numbers by 2 until you get a fraction.

Doing so, you get:

120 ÷ 2 = 60

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 2 = 7.5

7.5 cannot be a factor of 120 since it is a decimal number.

1. Now, proceed to the next prime number which is 3, and continue to divide till you get a fraction or 1. Doing so, you get:

15 ÷ 3 = 5

5 ÷ 3 = 1.66, which cannot be a factor

1. Therefore, when you move to the next prime number which is and continue the division process, you get:

5 ÷ 5 = 1

You have received 1 at the end in the division process and you cannot proceed further.

Hence, the prime factors of 120 are 2 × 2 × 2 × 3 × 5,

You can also write this as $2^{3}$ × 3 × 5. Here, the numbers 2, 3 and 5 are the prime numbers.

1. What are all the factors of 120?

The positive factors of 120 are called all the numbers that you use to divide the number 120 to get an even number. Here is the list of all the positive factors of  the number 120 in the numerical order:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120

The factors of 120 include negative numbers as well. Hence, all the positive factors of the number 120 can be converted to negative numbers. The list of all the negative factors of 120 is given below:

-1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60, and -120.

2. How many total factors of 120 are there?

According to the number theory, the prime factors of a positive integer are known as the prime numbers which divide that particular integer exactly. The prime factorization of a given positive integer is the list of all the integer's prime factors along with their multiplicities. The process of determining all these factors is known as integer factorization.

The factors of 120 are all the possible integers both the positive and the negative whole numbers which you can evenly divide into the number 120. The number 120 when divided by a factor of 120 will equal another factor of 120. When you count the total factors of 120 you will find that 120 has a total of 16 positive factors and 16 negative factors. Therefore, the total number of factors of the number 120 is 32.