In this lesson, we're going to look at different methods for finding the greatest common factor of two numbers. So what is the greatest common factor? It's the largest factor that the numbers have in common. So let's answer this question. What is the greatest common factor of 30 and 36? One way we can figure this out is by listing all the factors of both numbers. So here are all the factors of 30 - 1, 2, 3, 5, 6, 10, 15 and 30. And they would all pass the divisibility rules that we learned in our previous lesson. Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Now that we have all the factors listed for both numbers, we want to look and see what numbers they have in common. Well, they both have one, two, three and six as common factors. But the question is telling us to find the greatest common factor of the numbers. So we want to look for the largest factor that they have in common, which is the number six. So we can say that six is the greatest common factor between 30 and 36. Another way involves using the factor tree. Now, this method sometimes may seem to take a little bit more time, but you will find with more practice, it gets a lot easier and comes in handy, especially when you're working with big numbers. So we need to figure out the factor trees for 30 and 36 and then write them as prime factorization. So here's the factor tree for 30. Now we notice the end of each of the tree branches. We have two, three and five. So the prime factorization for 30 is two times three times five. We do the same thing for our other number, 36. And then we look at all the prime numbers at the end of the tree branches. Now we can write them out as a series of products. So two times two times three times three equals 36. Now, the next thing that we need to do is look to see which prime factors they have in common. Both numbers have a two and a three in common. Now, even though 36 has two twos and two threes, since 30 only has one two, we can only count that one number two, and it also has just one three. So we can only count one of those threes as well. So the only numbers that they really have in common are a two and a three. Now all we have to do is multiply the two and three together, we get six. That is our greatest common factor between the two numbers. So we list out the prime factorization for both numbers and we can use a factor tree to help us with that. And then we look to see what prime factors they have in common and then just multiply those together. So, to review, greatest common factor is the largest factor that the numbers have in common. And we have two methods that we can use. The first method involves listing all the factors of each number and then finding the largest factor that they have in common. The second method involves listing the prime factorization of each number. So we set up the factor tree and then list the prime factorization. And then we want to find the prime factors that they haven't common. And then lastly, multiply those prime factors together and that gives you the greatest common factor of those numbers.