Learn · Grades 6–8

How to Find the Prime Factorization of a Number

A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11, …). The prime factorization of a number writes it as a product of primes, and every number above 1 has exactly one.

Try it with your own problem ↓

The steps

  1. Start with the number. If it is prime, you are done.
  2. Find any prime that divides it evenly. Try 2, then 3, then 5, then 7, and so on. Quick tests: even numbers divide by 2; digits that add to a multiple of 3 divide by 3; numbers ending in 0 or 5 divide by 5.
  3. Divide, and write that prime down. You now have a smaller number.
  4. Repeat with the smaller number until you reach 1 (or until the last number is itself prime).
  5. Write the primes as a product, using exponents for repeats.

A worked example

Find the prime factorization of 360.

  1. 360 is even: 360 ÷ 2 = 180.
  2. 180 is even: 180 ÷ 2 = 90.
  3. 90 is even: 90 ÷ 2 = 45.
  4. 45 is odd, but its digits add to 9, so 45 ÷ 3 = 15.
  5. 15 ÷ 3 = 5.
  6. 5 is prime. The primes used are 2, 2, 2, 3, 3, 5.

360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5. Check: 8 × 9 × 5 = 360. ✓

Try it with your own problem

Open the free The Factor Tree with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: prime factorization 360Opens The Factor Tree with this example

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Common mistakes

Questions people ask

Is 1 a prime number?

No. A prime needs exactly two different factors, and 1 has only one.

What is a factor tree?

A drawing that splits a number into any two factors, then splits those, until all the leaves are prime. You get the same primes whichever split you start with.

What do I use prime factorization for?

Simplifying fractions, finding the GCF and LCM, and simplifying square roots.

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