Factors of 120

Let’s learn about what prime factorisation means. Prime factorization is the process of figuring out the prime numbers which, when multiplied together, can form the original number. Prime factorization is useful for coders who wish to make a unique code out of numbers that aren’t too large for computers to store or process rapidly. You might not always realize basic maths principles when you use them in real life, just as you probably don't notice the alphabet every time you read. Factoring is a fundamental maths concept that reverses multiplication by identifying the integers that multiply to form a larger number. This concept has obvious real-world applicability.

Prime Factorisation 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. Many different factors are commonly used in mathematical calculations, for example, the factors of the numbers 56, 90, etc. The prime factors of the number 120 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 factorisation 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 factorisation of 120, and the prime factorisation of 120 using a factor tree.

Factor Pairs of 120

The factor pairs of 120 refer 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 are 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 by 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 Factorisation 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 continuing 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.

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

15 ÷ 3 = 5

5 ÷ 3 = 1.66, which cannot be a factor

3. 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 of 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

2³× 3 × 5. 

Here, the numbers 2, 3 and 5 are the prime numbers.

Conclusion

This is all about factors of 120. Do remember to revise what you have learned and most importantly practice. For more such interesting topics, worksheets, and study materials you can visit our website and check them out.