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
Greatest Common Factor with Variables Practice Test:

#1:

Instructions: Find the greatest common factor (GCF).

a) 28x2y3, 21x2y, 70x2

b) 90a3b3, 10a4b2, 20a2b2


#2:

Instructions: Find the greatest common factor (GCF).

a) 12yz3, 48y2x2z, 28y3, 48y4x


#3:

Instructions: Find the greatest common factor (GCF).

a) 36xy8z6, 24xyz11, 42xy4z7, 30xyz6


#4:

Instructions: Find the greatest common factor (GCF).

a) 60x4y9z3, 120x9y3z2, 50x4y3z3, 150x5y3z2


#5:

Instructions: Find the greatest common factor (GCF).

a) 18j3k5, 72jk3h4, 24j2k3, 66jk2h


Written Solutions:

#1:

Solutions:

a) 7x2

b) 10a2b2


#2:

Solutions:

a) 4y


#3:

Solutions:

a) 6xyz6


#4:

Solutions:

a) 10x4y3z2


#5:

Solutions:

a) 6jk2