Example 2 Finding the Greatest Common Factor (GCF)
Greatest Common Factor
Welcome to MooMooMath. Today we are going to talk about the greatest common factor. Here are our first examples in fast form. Let’s look at 30 the first thing I’m going to factor is 5 times 6, the 5 is prime so I don’t bring it down, next 6 equals it 3 three times 2 so I write a 5 times 2 times 3. Now let’s do a factor three of 42, that 6 times 7, 6 is composite and 7 is prime so I’m done with that one so now I can factor the 6 down to 2 times 3 so the prime factorization is 2 times 3 times 7, so I circle my common factors and multiply so my greatest common factor is 6. Now let’s slow it down and look at the rules of greatest common factor.
1. Complete prime factorization for each number. This includes drawing a factor tree for each number and factor down to prime numbers.
2. Pair the common factoring. ( It may help to circle all the factors that are common )
3. Take the common factors (the ones that you circled) and multiple them back together and this gives you your GCF.
So let’s take it slowly with our steps in an example. The first step is beginning our prime factorization. The last time I took 5 times 6 but this time I’m going to factor it differently I’m going to do 2 times 15 just to show you a different method. OK 2 is prime, so I’m finished with that stem so I draw another stem off the 15 and it factors into 5 times 3. Notice that I end up with the same prime factorization that I had before. It is 2 times 5 times 3. Now let’s go over here and complete the prime factorization for 42. Since 42 is an even number I will write 2 down. That is 2 times 21 and the 21 factors into 3 times 7 so those are my three factors 2 times 3 times 7. So this completes step one, I have completed my prime factorization. Now I will circle the common factors. Both 30 and 42 have 2 as a common factor and both 30 and 42 have three as a common factor so all I do is multiply 2 times 3 and that gives me my GCFof 6 Hope this was helpful.