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# Lesson 64:  Greatest Common Factors

In this easy lesson, you'll learn an important concept about factors which is used again and again.

In division, a factor of a number is a number that divides evenly into it.  For example, 3 is a factor of 12, because 3 divides evenly into 12.  Let's list the factors of 24:  1, 2, 3, 4, 6, 8, 12, 24.  All of these numbers divide evenly into 24, so they are all factors of 24.

Very often in math we need to find a number that is a factor of two different numbers.  For example.  What are factors of both 18 and 30?  The factors of 18 are 1, 2, 3, 6, 9, and 18.  The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.  The two numbers have several factors in common.  What we are usually interested in, though, is the greatest common factor (GCF).  In this case, the GCF is 6.

Let's try one more.  What is the GCF of 24 and 40?  If you list the factors of each, which you should do for practice, you will see that it is 8.

Later you will have much more practice with this topic.  For now, just make sure that you understand the general concept, and that you feel comfortable listing factors of any number.

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