Online Pre-Algebra Tutoring: Factoring the Prime

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Prime factorization of a whole number means to write it as the product of only prime numbers.  A composite number can be written as a product of all of its prime factors.

To find the prime factorization of a number:

Divide the number by prime factors until the quotient is 1.

Let’s understand with an example

What is the prime factorization of 45?

45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

The prime factorization of 45 is:
45 = 3 × 3× 5

This can also be written using exponents as:
45 = 32 × 5

Factor Trees

Another method for producing the prime factorization of a natural number is to use what is called a factor tree.

A factor tree is a tool that breaks down any number into its prime factors

The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring. These two factors are the first branching in the factor tree. There are often several different pairs of factors that we could choose to begin the process. The choice does not matter; we may begin with any two factors. We repeat the process with each factor until each branch of the tree ends in a prime. Then the prime factorization is complete.

Example: Prime factorization of 24

Prime-factorization

The prime factorization is the product of the circled primes

So the prime factorization of 24 is 24 = 2 ×2 ×2 × 3 = 23 × 3.

Check Point

  1. What is the prime factorization of 86?
  2. What is the prime factorization of 592?
  3. What is the prime factorization of 225?
  4. What is the prime factorization of 1050?
  5. What is the prime factorization of 42 use the factor tree method
Answer Key
  1. 2 × 43
  2. 2×  2 × 2×  2 × 37 = 24 × 37
  3. 3 × 3 × 5 × 5 = 32 × 52
  4.  2 × 3 × 5 × 5 × 7 = 2 × 3 × 52 × 7
  5. Prime factorization1Prime factorization of 42 = 2×3×7

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