Yesterday, we reviewed how to factor a number. Today, we’re going to use that skill to work on determining the greatest common factor (GCF) for two numbers. This skill is most often useful when trying to come up with a common denominator for two fractions that you want to add or subtract.
Let’s find the GCF for 12 and 15.
Yesterday, we factored out 12. Let’s review that list.
12: 1, 2, 3, 4, 6, 12
Now, let’s factor 15. We have the identity factors of 1 and 15. A quick run through the rules of divisibility tells us that 15 is divisible by 3 and 5. Let’s look at our factor list for 15.
15: 1, 3, 5, 15
To determine the greatest common factor for 12 and 15, we stack the two lists.
12: 1, 2, 3, 4, 6, 12
15: 1, 3, 5, 15
Now we determine what numbers are on both lists.
12: 1, 2, 3, 4, 6, 12
15: 1, 3, 5, 15
Both 1 and 3 are bolded on both lists, but becasue 3 is the larger number, it is the greatest common factor of 12 and 15.
