6 — Factors and Prime Numbers

Factors and Prime Numbers

Solution & Explanation · ID: A7A88604

Question

Find the prime factorization of 72.

Hint

Start by dividing by the smallest prime numbers first.

Concept

Prime factorization breaks a number down into its prime factors. We repeatedly divide by the smallest prime factor until we reach 1.

Show Answer

72 = 2³ × 3²

Show Solution
1

Start with 72. Divide by 2: 72 ÷ 2 = 36

2

Continue with 36. Divide by 2: 36 ÷ 2 = 18

3

Continue with 18. Divide by 2: 18 ÷ 2 = 9

4

9 is not divisible by 2. Divide by 3: 9 ÷ 3 = 3

5

Continue with 3. Divide by 3: 3 ÷ 3 = 1

6

Prime factorization: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²

A factor tree showing 72 at the top. It branches down to 2 and 36. The 36 branches to 2 and 18. The 18 branches to 2 and 9. The 9 branches to 3 and 3. The prime factors 2, 2, 2, 3, and 3 are circled at the bottom. Below the tree is the final answer: 72 = 2³ × 3².