Home > Pre-algebra > Factors and Multiples > Prime Factorization
More Examples

## Prime Factorization

#### Introduction

Prime Factorization is expressing a number as a product of its prime factors. For example, the prime factorization of the number 18 can be written as $2 \ast 3 \ast 3$ or $3^{2} \ast 2$.#### Terms

**Factor**- Factors are numbers multiplied together to get another number. Because 3 * 4 = 12, both 3 and 4 are factors of 12.

**Prime**- A prime number is a number that only has 1 and itself as factors.

**Prime Factor**- A prime factor is a factor that is also a prime number.

## Lesson

To find the prime factorization for a given postive integer, we use what is called a factor tree, which looks like this for the number 12:

The prime factors are represented by the circled values, 2, 2, and 3. So for 12, the prime factorization is $2 \ast 2 \ast 3$, or $2^{2} \ast 3$.

If a numberâ€™s only factors are only 1 and itself, then that number is a prime number and no further factorization is possible.

## Examples

#### Prime Factorization of 12

Find the Prime Factorization

The prime factorization of 12 can be written as:

#### Prime Factorization of 72

Find the Prime Factorization

The prime factorization of 72 can be written as:

#### Prime Factorization of 61

Find the Prime Factorization

The factors of are . Therefore is a prime number.