Prime Factorization

How to find the prime factorization of a number: 2 examples their solutions.

Example 1

Example

Solution

Change 60 to a product of two factors.
60 = 6⋅10

Factors of a Number

Change 6 and 10 to products of two factors.
6 = 2⋅3
10 = 2⋅5

Repeat this until only prime numbers remain.

2⋅3⋅2⋅5
2, 3, and 5 are all prime.
Then combine and arrange the factors.
There are two 2s.
So write 22.
And write ⋅3⋅5.

So 22⋅3⋅5 is the prime factorization of 60.

Example 2

Example

Solution

Change 200 to a product of two factors.
200 = 2⋅100

2 is a prime.
So change 100 to a product of two factors.
100 = 10⋅10

Repeat this until only prime numbers remain.

Change the two 10s to a product of two factors.
10 = 2⋅5

2⋅2⋅5⋅2⋅5
2 and 5 are all prime.
Then combine and arrange the factors.
There are three 2s.
So write 23.
And there are two 5s.
So write ⋅52.

So 23⋅52 is the prime factorization of 200.