Worked Example 1
Using the GCF
Rewrite 36 + 48 as a common factor times a sum.
- 1The GCF of 36 and 48 is 12.
- 236 = 12 × 3 and 48 = 12 × 4
- 336 + 48 = 12(3 + 4)
Answer: 12(3 + 4)
Florida Grade 6 Math · Number Sense and Operations
MA.6.NSO.3.2: Factoring Out a Common Factor
What this Grade 6 benchmark means, worked examples, common mistakes, and a free printable worksheet.
Created by a Florida mom · Published by Tropical Learning LLC
What Is Benchmark MA.6.NSO.3.2?
Students rewrite the sum of two composite numbers as a common factor times a sum, using the distributive property. For example, 36 + 48 = 12(3 + 4).
Using the greatest common factor gives the simplest form, but any common factor works. This is the same skill students later use to factor algebraic expressions like 12x + 18.
Official benchmarkRewrite the sum of two composite whole numbers having a common factor, as a common factor multiplied by the sum of two whole numbers.
On the FAST test: part of the Grade 6 reporting category Number Sense and Operations, which is about 33–42% of the test.
Worked Examples
Worked Example 2
Another Common Factor
Rewrite 24 + 60 two different ways.
- 1Using the GCF, 12: 24 + 60 = 12(2 + 5)
- 2Using 6: 24 + 60 = 6(4 + 10)
- 3Check: 12 × 7 = 84 and 6 × 14 = 84
Answer: 12(2 + 5) or 6(4 + 10)
Common Mistakes to Watch For
Dividing only one number
Wrong:36 + 48 = 12(3 + 48)
Divide both numbers by the factor: 36 ÷ 12 = 3 and 48 ÷ 12 = 4, so 12(3 + 4).
Adding the factor instead of multiplying
Wrong:36 + 48 = 12 + (3 + 4)
The factor multiplies the sum: 12(3 + 4) = 12 × 7 = 84.
Helpful Math Tip
Check by multiplying back out: 12(3 + 4) = 36 + 48. If you get the original sum, the rewrite is right.
Related Grade 6 Skills
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