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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∗3∗32 ast 3 ast 3 or 32∗23^{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:

262312

The prime factors are represented by the circled values, 2, 2, and 3. So for 12, the prime factorization is 2∗2∗32 ast 2 ast 3, or 22∗32^{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

1212
2612
12=2∗612 = 2 * 6
262312
6=2∗36 = 2 * 3
The prime factorization of 12 can be written as:
22∗312^{2} * 3^{1}

Prime Factorization of 72

7272
23672
72=2∗3672 = 2 * 36
23621872
36=2∗1836 = 2 * 18
2362182972
18=2∗918 = 2 * 9
236218293372
9=3∗39 = 3 * 3
The prime factorization of 72 can be written as:
23∗322^{3} * 3^{2}

Prime Factorization of 61

6161
The factors of 6161 are 1 and 611\text{ and }61. Therefore 6161 is a prime number.

Prime Factorization Worksheets (PDF)

Prime Factorization Worksheet 1

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Prime Factorization Worksheet 2

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Prime Factorization Worksheet 3

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