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Wize High School Grade 10 Math Textbook > Algebra - Factors & Multiples of Numbers

Prime Factorization

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Prime Factorization

To write the prime factorization of a whole number, we need to rewrite that number into a product of prime numbers.

Examples
  • The prime factorization of 44 is
    2 x 2
  • The prime factorization of 1010 is
    2 x 5
This can get tricky when the number we want to find the prime factorization of is very large.

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Factor Tree

A factor tree is a tool that helps us find the prime factorization of a number visually.
  • At each level of the factor tree, we rewrite the previous number as a product of 2 numbers
  • We continue drawing more levels, stopping only when we've reached a prime number
  • The prime factorization of a number is the product of all of the prime numbers at the bottom of the factor tree

Example
Draw a factor tree to determine the prime factorization of 5400.
Therefore, the prime factorization of 5400 is 2×3×3×3×2×5×2×52\times 3\times3\times3\times2\times5\times2\times5.

Rewriting this using exponents, we see that the prime factorization is 23×33×52\boxed{2^3\times3^3\times5^2}.

Practice: Prime Factorization

Write the prime factorization of 6930.