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Common Factors Worksheet

A Grade 10 math worksheet focusing on finding common factors of numbers and algebraic expressions.

Grade 10 Math AlgebraFinding Common Factors
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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.APR.A.1CCSS.MATH.CONTENT.HSA.SSE.A.1.A
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Common Factors Worksheet

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Read each question carefully and determine the common factors as instructed. Show all your work.

1. List all the common factors of 24 and 36.

2. What is the greatest common factor (GCF) of 48 and 72?

3. The prime factorization of 60 is  . The prime factorization of 90 is  . The GCF of 60 and 90 is  .

4. If the prime factorization of number A is 2² × 3 × 5 and number B is 2 × 3² × 7, then their GCF is  .

5. What is the greatest common monomial factor of 12x³y² and 18x²y⁴?

a

6x²y²

b

6x³y⁴

c

3x²y²

d

12x³y⁴

6. Factor the expression 5a²b - 15ab² completely by factoring out the GCF.

7. Find the GCF of the terms in the polynomial 6x³ + 9x² - 12x and then factor the polynomial.

8. The GCF of two prime numbers is always 1.

T

True

F

False

9. The GCF of x²y and xy³ is xy.

T

True

F

False

10. Find the greatest common factor of the terms in the expression 24a²b³c⁴ + 36a³b²c + 60a⁴bc².