The greatest common factor (GCF), also known as the greatest common divisor (GCD) is the largest number that is a factor or divisor for a group of numbers. For example, the greatest common factor for 6, 24, and 51 is 3. This is the largest number that is a factor of all three numbers.

Test Objectives
• Demonstrate the ability to find the prime factorization of a whole number
• Demonstrate the ability to find the GCF for two numbers
• Demonstrate the ability to find the GCF for more than two numbers
GCF Practice Test:

#1:

Instructions: Find the Greatest Common Factor (GCF) for each group of numbers.

a) GCF(26, 65)

b) GCF(100, 75)

#2:

Instructions: Find the Greatest Common Factor (GCF) for each group of numbers.

a) GCF(87, 406)

b) GCF(1085, 117)

#3:

Instructions: Find the Greatest Common Factor (GCF) for each group of numbers.

a) GCF(805, 322, 4025)

#4:

Instructions: Find the Greatest Common Factor (GCF) for each group of numbers.

a) GCF(1620, 300, 1500, 3900)

#5:

Instructions: Find the Greatest Common Factor (GCF) for each group of numbers.

a) GCF(2400, 3150, 6300)

Written Solutions:

#1:

Solutions:

a) GCF(26, 65) = 13

b) GCF(100, 75) = 25

#2:

Solutions:

a) GCF(87, 406) = 29

b) GCF(1085, 117) = 1

#3:

Solutions:

a) GCF(805, 322, 4025) = 161

#4:

Solutions:

a) GCF(1620, 300, 1500, 3900) = 60

#5:

Solutions:

a) GCF(2400, 3150, 6300) = 150