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
Finding the Greatest Common Factor (GCF) Test:
#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}
#2:
Instructions: Find the greatest common factor (GCF).
a) 12yz^{3}, 48y^{2}x^{2}z, 28y^{3}, 48y^{4}x
#3:
Instructions: Find the greatest common factor (GCF).
a) 36xy^{8}z^{6}, 24xyz^{11}, 42xy^{4}z^{7}, 30xyz^{6}
#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}
#5:
Instructions: Find the greatest common factor (GCF).
a) 18j^{3}k^{5}, 72jk^{3}h^{4}, 24j^{2}k^{3}, 66jk^{2}h
Written Solutions:
Solution:
a) 7x^{2}
b) 10a^{2}b^{2}
Solution:
a) 4y
Solution:
a) 6xyz^{6}
Solution:
a) 10x^{4}y^{3}z^{2}
Solution:
a) 6jk^{2}