Finding prime factors

Prime factors are factors of a number that are, themselves, prime numbers.

Sometimes you might be asked to write a number as the product of its prime factors.

There are many methods to find the prime factors of a number, but one of the most common is to use a prime factor tree:

  • Start the factor tree using any pair of factors (two numbers that multiply together to make your number).
  • If one of these factors is prime, that branch ends.
  • If a factor isn't prime, divide it into a factor pair.
  • The branches continue to expand until all the factors are prime numbers.
  • The final answer is the list of all the prime numbers displayed at the end of these branches.

curriculum-key-fact
Note that the number \({1}\) is not used within a factor tree.

Example:

Write 24 as the product of its prime factors.

Factor tree diagram

Write 24 as the product of its prime factors

You could choose any factor pair to start.