Greatest Common Factor (GCF) of Monomials Worksheet

Practice finding the Greatest Common Factor (GCF) of monomials, including those with multiple variables and exponents, suitable for Grade 12 Algebra students.

Grade 12 Math AlgebraGreatest Common Factor (GCF) of Monomials

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Includes

Fill in the BlanksMultiple Choice2 Short AnswerTrue / False

Standards

CCSS.MATH.CONTENT.HSA.SSE.A.2CCSS.MATH.CONTENT.HSA.APR.A.1

Topics

MathAlgebraGCFMonomialsFactoring

7 sections · Free to use · Printable

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Greatest Common Factor (GCF) of Monomials

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Read each question carefully and determine the Greatest Common Factor (GCF) for the given monomials. Write your answers in the space provided.

1. The GCF of 12x³y² and 18x²y⁵ is .

2. For the monomials 24a⁴b³c and 36a²b⁶, the GCF is .

3. The GCF of -15m³n²p and 25m²n⁴ is .

4. Which of the following is the GCF of 40r²s³t and 60r⁴st²?

20r²s

20r⁴s³t²

10r²st

20r²s²t

5. The GCF of the monomials 7p²q³, 14pq², and 21p³q is:

7pq

7p³q³

7pq²

21p³q³

6. Find the GCF of 32x²y³z⁴, 48xy⁵z², and 80x³y²z³.

7. Explain the steps you would take to find the GCF of three monomials.

8. The GCF of 6a²b and 10ab³ is 2ab.

True

False

9. If two monomials have no common variables, their GCF is always a constant.

True

False

10. The area of a rectangle is given by the monomial 30x⁵y⁴. If the length of the rectangle is 6x²y, what is the GCF of the length and the area?