What is the prime factorization of 120 and how do you get the answer?

Answer 1

Start by listing out all pairs of numbers greater than 0 and less than or equal to 120 that have a product equal to 120:

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

So, there are 8 factor pairs of 120. Now, show the prime factorization for 120 by expressing it as the product of ALL prime numbers:

120 = 2 x 60 <--- 2 is a prime number

Next step is to reduce 60 to the product of prime numbers: 60 = 3 x 20 <--- 3 is a prime number.

Next step is to reduce 20 to the product of prime numbers: 20 = 5 x 4 <--- 5 is a prime number.

Next step is to reduce 4 to the product of prime numbers: 4 = 2 x 2 <--- 2 is a prime number.

The final step is to reduce 2 to the product of prime numbers:

• So, the prime factorization is as follows: 120 = 2 x 2 x 2 x 3 x 5