Learn about Applications of Greatest Common Factor Now let’s do word problems on greatest common factors. The problem says that Stella is making fruit baskets. She has 30 apples, 24 bananas and 12 oranges. What the greatest number of baskets she can make if each type of fruit is distributed equally? What she means to say is; if she has 30 apples, 24 bananas and 12 oranges, how many baskets can we make where each basket has to have the same number of oranges, bananas and apples? One basket can have four oranges, four oranges and four oranges. This has to be divided equally among all the baskets, so do bananas and so do apples. Here is how we do them. First, we list the factors for 30, 24 and 12. What we do is we find factors for 30, 24 and 10 that are common. I will put 30, 24 and 12. Let’s see what factor, what number can we divide each one of these with which divides them completely. Let’s say I divide with two. If two is a factor to all three, I can divide 30, 24 and 12 with the same number too. What I am left with? 30÷2=15, 24÷2=12 and 12÷2=6. Step two; we continue doing this until we can't do it anymore. We've got 30, 24 and 12. We divide it by two to get 15, 12 and six. Can we divide by any other common factor? What's a number that divides all three of this? I can divide it by three. 15÷3=5, 12÷3=4, 6÷3=2. I'm left with five, four and two. Is there a number which is not one of course which can divide all three? I can't find one. Step three, the greatest common factor for all these three numbers is the multiplication or the product of the common factors, so GCF of 30, 24 and 12 is 2×3=6. The GCF are these three number is six. What that means is that Stella can make six baskets. How much will each basket have? Each basket will have 30÷6 which is five apples, 24÷6 which is four bananas and 12÷6 which is two oranges each. Each basket will have these. All six baskets will be absolutely the same.