Prime Factorization with Factor Trees (Grades 5–6)
Every whole number greater than 1 can be written as a product of prime numbers — its prime factorization — and there's only one way to do it (order aside).
Understanding prime factorization with factor trees
A factor tree helps: split the number into any factor pair, then keep splitting each branch until every leaf is prime. The primes at the bottom, multiplied together, rebuild the number.
Seeing it in action
Worked example
Prime-factorize 12.
12 → 2 × 6 → 6 splits into 2 × 3.
Primes: 2, 2, 3. So 12 = 2 × 2 × 3 (or 2² × 3).
12 splits to prime leaves 2 × 2 × 3.
A common mistake, and the fix
Stopping at a factor that isn’t prime.
12 = 2 × 6 is a correct product, but 6 isn’t prime, so split it again: 12 = 2 × 2 × 3. Check that every number at the bottom of the tree is prime and that they multiply back to 12.
Try a few
Prime-factorize 18
Prime-factorize 20
Prime-factorize 30
Factor Fields
A calm number-theory game for factors, multiples, primes, GCF, and LCM.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
Want a printable set too?
Practise this skill in Numeris, browse more free math pages, or join our optional resource updates.
All free math pages →