Module 3 · Factors and multiples · Lesson 10 of 39

Prime factorization

Break any composite number into a product of primes.

In this lesson · about 12 minutes

  • Tell factors from terms
  • Find a prime factorization with a factor tree
  • Write it with exponents

Factors are things that get multiplied together. (Things that get added are called terms.) The factors of 12 are 1, 2, 3, 4, 6 and 12.

A prime factorization writes a number as a product of primes only. For 12 that's 2 × 2 × 3, written compactly as 22 × 3: the small 2 is an exponent that says "two factors of 2". We list primes from smallest to largest.

Try it · interactive

Factor tree

Type any number. Keep splitting until every branch ends in a prime.

Click a blue number to split it by its smallest prime. Green circles are prime and can't be split.

Worked example

Find the prime factorization of 45

Keep breaking the number into smaller factors until every factor is prime.

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    Tip: master each practice set first (get 5 right in a row).

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