SME
Grade 6 Math · Problem type
Factor expressions using the GCF
Use this for “Write 36 + 8 as a product of the GCF and a sum.”
Diagram
36 + 8 = 44.
This is an example. Type your own values to start a new problem.
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Formulas
greatest common factor of 36 and 8: 4
Greatest factor of both numbers = greatest common factor
36 ÷ 4 = 9
First number ÷ GCF = first number inside the parentheses
8 ÷ 4 = 2
Second number ÷ GCF = second number inside the parentheses
Assumptions
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Both numbers are multiples of their GCF, so the sum is the GCF times a sum.
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Multiplying back gives the same sum: 4 × 9 + 4 × 2 = 36 + 8.
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Whole numbers from 1 to 100.
Step-by-step
WE KNOW
First number: 36
Second number: 8
FIND
greatest common factor, first number inside the parentheses, second number inside the parentheses
Step 1 · Find greatest common factor
greatest common factor of 36 and 8: ?
Greatest factor of both numbers = greatest common factor
List the factors of each number and take the greatest one in both lists.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 8: 1, 2, 4, 8
Greatest common factor = 4
Step 2 · Find first number inside the parentheses
36 ÷ 4 = ?
First number ÷ GCF = first number inside the parentheses
How many of the GCF make the first number?
First number inside the parentheses = 9
Step 3 · Find second number inside the parentheses
8 ÷ 4 = ?
Second number ÷ GCF = second number inside the parentheses
How many of the GCF make the second number?
Second number inside the parentheses = 2 (36 + 8 = 4(9 + 2))
Check
Put the numbers back in. Both sides should match.
greatest common factor of 36 and 8: 4 ✓
4 × 9 = 36 ✓
4 × 2 = 8 ✓
Topic check
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