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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 number’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.
More Examples

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