Greatest Common Factors

Practice computing greatest common factors

The greatest common factor between two numbers is the largest number that both numbers is divisible by. These worksheets provide practice in this very important mathematics skill. A prerequisite to finding GCFs is being able to decompose an integer into primes, so if students are not good at this yet then this one may be over their heads.

Finding a GCF is a three step process, but all three steps are documented in the answer page that accompanies every LCM worksheet. First, both numbers need to be decomposed into their prime numbers. Next, the combination of primes that are present in both sets is assembled. Finally, the product (multiplication together) of all of these primes is the GCF. A GCF will never be less than one or larger than the smaller of the two numbers.

Students are easily confused with the difference between GCFs and Least Common Multiples (LCMs), as the steps and uses are similar. It would be a good idea to come back to both of these skills repeatedly over time in order to reinforce the students’ understanding of both.