Skip to Content

Examples: Factoring Numbers

The first 30 primes:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
31, 37, 41, 43, 47, 53, 59, 61, 67,
71, 73, 79, 83, 89, 97, 101, 103,
107, 109, 113

Prime Factorization

People write out their factoring work in a variety of ways. Below are a few.

To find the prime factors of a number:

  1. Divide the number by the smallest possible prime number.
  2. Divide the result by the smallest possible prime number.
  3. Continue until the result is also a prime number.

Divisibility Rules

If the number is even, the smallest possible prime factor will be 2.
If the number is not even, and you are not sure which is the smallest prime factor, divisibility rules may help.

Factor Tree

The following example breaks down a number into its prime factors using a tree diagram.

Find the prime factorization of 1092:

factor tree showing prime factors circled

Check the answer:
(2)(3)(2)(7)(13) = 1092

Here's a video of a factor tree for the number 392
Click the sideways triangle to play the video. The video has sound. (Text transcript >>)

 

 

Upside-Down Division

The following example breaks down a number into its prime factors using an upside-down division approach.

Find the prime factorization of 1050:

factors of 1050 shown in upside down division format

Check the answer:
(2)(3)(5)(5)(7) = 1050

Right-Side Up Division

The following example breaks down a number into its prime factors using a right-side-up division approach.

To find the factors using 'right-side up' division, leave yourself plenty of room above the original number on your working paper.

prime factorization of

Check the answer:
(3)(5)(5)(5)(7) = 2625

Vocabulary

Unable to select database