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Grade 5 Math · Level 1, Place Value & Powers of 10

Prime Factorization

How the lesson starts: Prime Factorization

1. The Number Forest

   Welcome to the Number Forest! Ranger Juniper plants number seeds. Each seed grows into a tree that splits into branches, until every leaf is a prime number. Today's seed is 72. What prime leaves will it grow?

2. A little tree

   Start small with 18. It splits into 2 × 9. 2 is prime, so it's a leaf. 9 splits again into 3 × 3. Now every leaf is prime. So 18 = 2 × 3 × 3. Two threes is 3², so 18 = 2 × 3².

3. Grow the 72 tree

   72 splits into 8 × 9. 8 becomes 2 × 2 × 2, and 9 becomes 3 × 3. Three twos and two threes: 2³ × 3². Watch out: 2³ means 2 × 2 × 2 = 8, not 2 × 3. Going back, 8 × 9 = 72!