Prime Factorization With Factor Trees

Start with Divisibility Rules Practice so students know which primes to try first. Then move from factor trees to the division method and finish with exponent form.

Finish factor trees for 70, 225 and 280 and write each prime factorization with exponents. A factor tree splits a number into factors until every branch ends in a prime: 36 = 2 × 2 × 3 × 3 = 2 2 × 3 2. The directions on the page read: Finish each factor tree until every branch ends in a prime number. Then write the prime factorization using exponents, from smallest to largest prime. An answer key is included.

Yes, both. We made it for 6th Grade factoring, and the page works the same whether it lands on a kitchen table or a center rotation. At home, most families go through it together and talk the answers out loud, and that talking is where most of the learning happens with divisibility and prime factorization. In class it runs well as independent work while you pull a small group. Print one copy or thirty, whichever the day needs.

It splits a number into two factors, then splits each factor again until every branch ends in a prime. The primes at the ends give the prime factorization, so 280 = 2 cubed × 5 × 7.

Exponents shorten repeated factors, so 2 × 2 × 2 × 5 = 2 cubed × 5. Long products become easier to read, as in 600 = 2 cubed × 3 × 5 squared.

The rules box lists 2, 3, 4, 5, 6, 9 and 10. For example, a number divides by 4 when its last two digits do, and by 6 when it divides by both 2 and 3.