Stretch: Factor Out the Greatest Common Factor
I can use the GCF and the distributive property to rewrite a sum like 36 + 24 as 12 × (3 + 2).
🧠 The Big Idea
Every sum of two whole numbers can be rewritten as GCF × (sum of what's left).
This is the distributive property running backward — called factoring.
Example: 36 + 24. GCF(36, 24) = 12. 36 ÷ 12 = 3 and 24 ÷ 12 = 2, so 36 + 24 = 12 × (3 + 2). Check: 12 × 5 = 60 ✓.
✏️ Your Turn
0 of 3 checks complete
1. Factor 18 + 30 using the GCF. GCF(18,30) = 6, so…
2. Which is a fully-factored form of 40 + 16? (use the greatest common factor)
3. Rewrite 27 + 45. GCF = 9. The factored form is…
💬 Explain Your Thinking
Pick your own sum and factor it. Explain each step:
"For blank + blank, the GCF is blank. Dividing each term gives blank and blank, so the factored form is blank × (blank + blank)."