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). 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.
Understanding prime factorization with factor trees
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). 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.
Key Idea
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). 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.
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.
Ready for the interactive lab?
Practice prime factorization with factor trees in Numeris with instant feedback.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesWant a printable set too?
Browse free math pages with separate student sheets and answer keys, or join our optional resource updates.
Looking for Grade 2 worksheets? →