6 — Factors and Prime Numbers

Factors and Prime Numbers

Solution & Explanation · ID: 27D73FCF

Question

Find the prime factorization of 40.

Hint

Use a factor tree or division method to break 40 down into prime factors.

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

40 = 2³ × 5

Show Solution
1

Start with 40. Divide by 2: 40 ÷ 2 = 20

2

Continue with 20. Divide by 2: 20 ÷ 2 = 10

3

Continue with 10. Divide by 2: 10 ÷ 2 = 5

4

5 is prime, so we stop. Prime factorization: 40 = 2 × 2 × 2 × 5 = 2³ × 5

A factor tree showing 40 at the top. It branches down to 2 and 20. The 20 branches to 2 and 10. The 10 branches to 2 and 5. The prime factors 2, 2, 2, and 5 are circled at the bottom. Below the tree is the final answer: 40 = 2³ × 5.