# 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 2^{2}.

And write ⋅3⋅5.

So 2^{2}⋅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 2^{3}.

And there are two 5s.

So write ⋅5^{2}.

So 2^{3}⋅5^{2} is the prime factorization of 200.