Free Printable WorksheetMathGrade 8Math Curriculum7.EE.A.1

8.83 Factoring Out the Greatest Common Factor Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.83 Factoring Out the Greatest Common Factor. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.83 Factoring Out the Greatest Common Factor - Which factored form correctly uses the greatest common factor? (CCSS 7.EE.A.1; CA 7.EE.A.1; MA 7.EE.A.1)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.83 Factoring Out the Greatest Common Factor skill assessments:

Problem 1Difficulty: Hard
Which option is the complete GCF factorization of 91u5v4 - 117u2v2, not just a partial factorization?
A13u2v2(7u3v2 - 9)
B13(7u5v4 - 9u2v2)
Cu2(91u3v4 - 117v2)
Du2v2(91u3v2 - 117)
Solution & Explanation:The full GCF is 13u2v2. After factoring it out, the expression inside the parentheses is 7u3v2 - 9, so the completely factored form is 13u2v2(7u3v2 - 9).
Problem 2Difficulty: Hard
Several factorizations of 24m3n4 - 54m2n3 + 18m2n2 are shown. Which one is equivalent to the original expression and leaves no common factor inside the parentheses?
A6m2n2(4mn2 - 9n + 3)
Bm2n2(24mn2 - 54n + 18)
C6m2n(4mn3 - 9n2 + 3n)
D6(4m3n4 - 9m2n3 + 3m2n2)
Solution & Explanation:The full GCF is 6m2n2. After factoring it out, the expression inside the parentheses is 4mn2 - 9n + 3, so the completely factored form is 6m2n2(4mn2 - 9n + 3).
Problem 3Difficulty: Hard
A diagram-free area model for 70m2n4 + 49n2 can be rewritten by taking out a common side length. Which factorization shows that GCF?
A7n2(10m2n2 + 7)
B7n2(10m2n2 + 8)
C7(10m2n4 + 7n2)
Dn2(70m2n2 + 49)
Solution & Explanation:The common side length or shared factor is 7n2. Factoring 7n2 out of each term in 70m2n4 + 49n2 leaves 10m2n2 + 7, so the total can be written as 7n2(10m2n2 + 7).

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 7.EE.A.1 (Primary standard selected for prompt fields: CCSS 7.EE.A.1. Skill statement: Which factored form correctly uses the greatest common factor? Associated standards listed with this skill: CCSS 7.EE.A.1; CA 7.EE.A.1; MA 7.EE.A.1. Use this embedded wording as the best available supporting standard description for this workflow.).

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