College Algebra Quiz: Factoring Out Greatest Common Factor Gcf
20 questions · exam conditions
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Factoring Out Greatest Common Factor GcfQuestion 1 of 20

Choose the correct GCF for 24a2b24a^2b and 36ab236ab^2, then factor it out.

12ab(2a+3b)12ab(2a+3b)
6ab(4a+6b)6ab(4a+6b)
24ab(a+b)24ab(a+ b)
18ab( 43a+2b)18ab( \,\frac{4}{3}a+2b)
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College Algebra Quiz

College Algebra Quiz: Factoring Out Greatest Common Factor Gcf

Practice Factoring Out Greatest Common Factor Gcf in College Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Factoring Out Greatest Common Factor Gcf, giving you a quick way to practice the rules, question types, and explanations that matter most for College Algebra.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Choose the correct GCF for 24a2b24a^2b and 36ab236ab^2, then factor it out.

  1. 12ab(2a+3b)12ab(2a+3b) (correct answer)
  2. 6ab(4a+6b)6ab(4a+6b)
  3. 24ab(a+b)24ab(a+ b)
  4. 18ab( 43a+2b)18ab( \,\frac{4}{3}a+2b)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given terms, 24a^2 b and 36a b^2, the GCF is 12ab, which, when factored out, results in the expression 12ab(2a + 3b). The correct choice, 12ab(2a+3b), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '6ab(4a+6b)', which misses the largest common factor. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 2

What is the GCF of the terms in 20x4y220x^4y^2 and 30x2y330x^2y^3?

  1. 10x2y210x^2y^2 (correct answer)
  2. 5x4y35x^4y^3
  3. 10x4y210x^4y^2
  4. 20x2y320x^2y^3
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. For the given terms, 20x^4 y^2 and 30x^2 y^3, the GCF is 10x^2 y^2. The correct choice, 10x^2 y^2, accurately represents the GCF, demonstrating understanding of the concept. A common mistake is selecting a non-greatest factor, seen in the distractor '5x^4 y^3', which does not divide both terms evenly. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 3

How can −12x2−18x-12x^2-18x be simplified by factoring out the GCF?

  1. −6x(2x+3)-6x(2x+3) (correct answer)
  2. 6x(−2x−3)6x(-2x-3)
  3. −12x(x+18)-12x(x+18)
  4. −3x(4x+18)-3x(4x+18)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, -12x^2 - 18x, the GCF is -6x (or equivalently 6x with negatives inside), which, when factored out, results in the expression -6x(2x + 3). The correct choice, -6x(2x+3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is ignoring the negative sign, seen in distractors that do not match the original expression. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 4

Factor out the GCF: 35x2y+49xy235x^2y+49xy^2.

  1. 7xy(5x+7y)7xy(5x+7y) (correct answer)
  2. 14xy(2.5x+3.5y)14xy(2.5x+3.5y)
  3. 7y(5x2+7xy)7y(5x^2+7xy)
  4. xy(35x+49y)xy(35x+49y)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 35x^2 y + 49x y^2, the GCF is 7x y, which, when factored out, results in the expression 7x y(5x + 7y). The correct choice, 7x y(5x + 7y), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x y(35x + 49y)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 5

Factor out the GCF: 4xy+8x2y24xy+8x^2y^2.

  1. 4xy(1+2xy)4xy(1+2xy) (correct answer)
  2. 2xy(2+4xy)2xy(2+4xy)
  3. 4x(y+2xy2)4x( y+2xy^2)
  4. 8xy(1+xy)8xy(1+x y)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 4x y + 8x^2 y^2, the GCF is 4x y, which, when factored out, results in the expression 4x y(1 + 2x y). The correct choice, 4x y(1 + 2x y), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '4x(y + 2x y2y^2)', which misses the common y in the second term properly. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 6

Which expression shows 3x2+6x3x^2+6x factored completely by its GCF?

  1. x(3x+6)x(3x+6)
  2. 3x(x+2)3x(x+2) (correct answer)
  3. 6x(x+2)6x(x+2)
  4. 3(x2+2x)3(x^2+2x)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 3x^2 + 6x, the GCF is 3x, which, when factored out, results in the expression 3x(x + 2). The correct choice, 3x(x + 2), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x(3x + 6)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 7

Identify the GCF and factor: 9x2+27x9x^2+27x.

  1. 9x(x+3)9x(x+3) (correct answer)
  2. 3x(3x+27)3x(3x+27)
  3. 27x(x+3)27x(x+3)
  4. x(9x+27)x(9x+27)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 9x^2 + 27x, the GCF is 9x, which, when factored out, results in the expression 9x(x + 3). The correct choice, 9x(x + 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x(9x + 27)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 8

Which expression shows 27x3y−9x2y27x^3y-9x^2y factored by its GCF?

  1. 9x2y(3x−1)9x^2y(3x-1) (correct answer)
  2. 27x2y(x−1)27x^2y(x-1)
  3. 9xy(3x2−x)9xy(3x^2-x)
  4. −9x2y(3x−1)-9x^2y(3x-1)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 27x^3 y - 9x^2 y, the GCF is 9x^2 y, which, when factored out, results in the expression 9x^2 y(3x - 1). The correct choice, 9x^2 y(3x - 1), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '9x y(3x23x^2 - x)', which misses the full variable power in the GCF. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 9

Identify the GCF and factor: 6x4+9x36x^4+9x^3.

  1. 3x3(2x+3)3x^3(2x+3) (correct answer)
  2. 6x3(x+3)6x^3(x+3)
  3. 3x(2x3+3x2)3x(2x^3+3x^2)
  4. x3(6x+9)x^3(6x+9)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 6x^4 + 9x^3, the GCF is 3x^3, which, when factored out, results in the expression 3x^3(2x + 3). The correct choice, 3x^3(2x + 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '3x(2x32x^3 + 3x23x^2)', which misses the full variable power in the GCF. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 10

What is the GCF of the terms in 27r2s27r^2s and 9rs39rs^3?

  1. 9rs9rs (correct answer)
  2. 27rs327rs^3
  3. 9r2s39r^2s^3
  4. 3rs3rs
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. For the given terms, 27r^2 s and 9r s^3, the GCF is 9r s. The correct choice, 9r s, accurately represents the GCF, demonstrating understanding of the concept. A common mistake is selecting a smaller factor, seen in the distractor '3r s', which misses the largest coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 11

Which shows 2x2y+8xy2x^2y+8xy factored completely by its GCF?

  1. 2xy(x+4)2xy(x+4) (correct answer)
  2. xy(2x+8)xy(2x+8)
  3. 2x(xy+4y)2x(xy+4y)
  4. 8xy( 14x+1)8xy(\,\frac{1}{4}x+1)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 2x^2 y + 8x y, the GCF is 2x y, which, when factored out, results in the expression 2x y(x + 4). The correct choice, 2x y(x+4), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x y(2x+8)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 12

Which expression shows 15xy+20y15xy+20y factored completely by its GCF?

  1. 5y(3x+4)5y(3x+4) (correct answer)
  2. y(15x+20)y(15x+20)
  3. 5xy(3+4)5xy(3+4)
  4. 10y(3x+2)10y(3x+2)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 15x y + 20 y, the GCF is 5 y, which, when factored out, results in the expression 5 y(3x + 4). The correct choice, 5 y(3x + 4), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'y(15x + 20)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 13

Which expression shows 8x4+12x28x^4+12x^2 factored completely by its GCF?

  1. 4x2(2x2+3)4x^2(2x^2+3) (correct answer)
  2. 2x2(4x2+12)2x^2(4x^2+12)
  3. 8x2(x2+12)8x^2(x^2+12)
  4. x2(8x2+12)x^2(8x^2+12)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 8x^4 + 12x^2, the GCF is 4x^2, which, when factored out, results in the expression 4x^2(2x22x^2 + 3). The correct choice, 4x^2(2x22x^2 + 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x^2(8x28x^2 + 12)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 14

Identify the GCF and factor: 18a2b+24ab218a^2b+24ab^2.

  1. 6ab(3a+4b)6ab(3a+4b) (correct answer)
  2. 12ab(3a+2b)12ab(3a+2b)
  3. 6a(3ab+4b2)6a(3ab+4b^2)
  4. ab(18a+24b)ab(18a+24b)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 18a^2 b + 24a b^2, the GCF is 6a b, which, when factored out, results in the expression 6a b(3a + 4b). The correct choice, 6a b(3a + 4b), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'a b(18a + 24b)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 15

Which of the following shows 12x2+18x12x^2+18x factored by its GCF?

  1. 6x(2x+3)6x(2x+3) (correct answer)
  2. 3x(4x+6)3x(4x+6)
  3. 12x(x+18)12x(x+18)
  4. x(12x+18)x(12x+18)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 12x^2 + 18x, the GCF is 6x, which, when factored out, results in the expression 6x(2x + 3). The correct choice, 6x(2x + 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '3x(4x + 6)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 16

Factor out the GCF: 45ab−30a45ab-30a.

  1. 15a(3b−2)15a(3b-2) (correct answer)
  2. 5a(9b−6)5a(9b-6)
  3. 30a(1.5b−1)30a(1.5b-1)
  4. 15ab(3−2)15ab(3-2)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 45a b - 30a, the GCF is 15a, which, when factored out, results in the expression 15a(3b - 2). The correct choice, 15a(3b - 2), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '5a(9b - 6)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 17

Identify the GCF and factor: 32p3q+48p2q232p^3q+48p^2q^2.

  1. 16p2q(2p+3q)16p^2q(2p+3q) (correct answer)
  2. 8p2q(4p+6q)8p^2q(4p+6q)
  3. 16pq(2p2+3pq)16pq(2p^2+3pq)
  4. 48p2q(p+q)48p^2q(p+q)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 32p^3 q + 48p^2 q^2, the GCF is 16p^2 q, which, when factored out, results in the expression 16p^2 q(2p + 3q). The correct choice, 16p^2 q(2p + 3q), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '8p^2 q(4p + 6q)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 18

Which of the following shows 2x2y+6xy22x^2y+6xy^2 factored by its GCF?

  1. 2xy(x+3y)2xy(x+3y) (correct answer)
  2. xy(2x+6y)xy(2x+6y)
  3. 2y(x2+3xy)2y(x^2+3xy)
  4. 6xy(x+y)6xy(x+y)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, (2x22x^2 y + 6x y2y^2), the GCF is (2xy), which, when factored out, results in the expression (2xy(x + 3y)). The correct choice, (2xy(x + 3y)), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in distractors like (xy(2x + 6y)) or (2y(x2x^2 + 3xy)), which miss the largest common factor. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 19

Factor out the GCF: 63a3−42a263a^3-42a^2.

  1. 21a2(3a−2)21a^2(3a-2) (correct answer)
  2. 7a2(9a−6)7a^2(9a-6)
  3. 42a2(1.5a−1)42a^2(1.5a-1)
  4. a2(63a−42)a^2(63a-42)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 63a^3 - 42a^2, the GCF is 21a^2, which, when factored out, results in the expression 21a^2(3a - 2). The correct choice, 21a^2(3a - 2), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor '7a^2(9a - 6)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.

Question 20

Which of the following shows 6x2y+9xy6x^2y+9xy factored by its GCF?

  1. 3xy(2x+3)3xy(2x+3) (correct answer)
  2. 6xy(x+3)6xy(x+3)
  3. 3y(2x2+3x)3y(2x^2+3x)
  4. xy(6x+9)xy(6x+9)
Explanation: This question tests college-level algebra skills in factoring out the Greatest Common Factor (GCF). The concept involves identifying the largest factor shared among terms and using it to simplify expressions. In the given expression, 6x^2 y + 9x y, the GCF is 3x y, which, when factored out, results in the expression 3x y(2x + 3). The correct choice, 3x y(2x + 3), accurately represents the factorization, demonstrating understanding of the GCF concept. A common mistake is partial factorization, seen in the distractor 'x y(6x + 9)', which misses the largest common coefficient. To support students, emphasize practice with identifying GCF through various expressions, and reinforce the importance of checking work for complete factorization. Encourage exercises in different contexts to strengthen recognition of common factors.