### About Greatest Common Factor with Variables:

In prealgebra we learned how to find the greatest common factor or GCF for a group of numbers. Here we will expand on this topic and learn how to find the greatest common factor or GCF for a group of terms. We will rely on this skill heavily once we get into factoring in the next section.

Test Objectives

- Demonstrate a general understanding of the meaning of the greatest common factor (GCF)
- Demonstrate the ability to find the greatest common factor (GCF) for a group of numbers
- Demonstrate the ability to find the greatest common factor (GCF) for a group of terms

#1:

Instructions: Find the greatest common factor (GCF).

a) 28x^{2}y^{3}, 21x^{2}y, 70x^{2}

b) 90a^{3}b^{3}, 10a^{4}b^{2}, 20a^{2}b^{2}

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#2:

Instructions: Find the greatest common factor (GCF).

a) 12yz^{3}, 48y^{2}x^{2}z, 28y^{3}, 48y^{4}x

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#3:

Instructions: Find the greatest common factor (GCF).

a) 36xy^{8}z^{6}, 24xyz^{11}, 42xy^{4}z^{7}, 30xyz^{6}

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#4:

Instructions: Find the greatest common factor (GCF).

a) 60x^{4}y^{9}z^{3}, 120x^{9}y^{3}z^{2}, 50x^{4}y^{3}z^{3}, 150x^{5}y^{3}z^{2}

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#5:

Instructions: Find the greatest common factor (GCF).

a) 18j^{3}k^{5}, 72jk^{3}h^{4}, 24j^{2}k^{3}, 66jk^{2}h

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Written Solutions:

#1:

Solutions:

a) 7x^{2}

b) 10a^{2}b^{2}

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#2:

Solutions:

a) 4y

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#3:

Solutions:

a) 6xyz^{6}

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#4:

Solutions:

a) 10x^{4}y^{3}z^{2}

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#5:

Solutions:

a) 6jk^{2}