Question

Find the GCF 8x and 22xy.

Answer 1

First find the greatest common factor of 8 and 22.

To find the greatest common factor of 8,

begin by dividing 8 by all the numbers you can.

8 ÷ 1 = 8

8 ÷ 2 = 4

Notice that I stopped here because if I continued

dividing, I would be dividing 8 by 4 which is 2.

Make sure to stop dividing when you see numbers repeat.

So the factors of 8 are 1, 2, 4, and 8.

Now do the same thing for 22.

22 ÷ 1 = 22

22 ÷ 11 = 2

So the factors of 22 are 1, 2, 11, and 22.

Now look for the largest number shared by the two lists.

In this case, the largest number is 2.

Now let's move to the variables.

To qualify for the Greatest Common Factor,

the variable must appear in every monomial.

Since the y doesn't appear in every monomial, it doesn't qualify.

However, notice that the x does appear in every monomial.

If the variable does appear in every monomial, the Greatest

Common Factor will use the smallest power on that variable.

Since the smallest power for x in both monomials is x, we use x.

So our greatest common factor is 2x.

Answer 2

2x

Explanation:

Factor both terms given to simplest terms:

8x = 2 * 2 * 2 * x

22xy = 2 * 11 * x * y

Note that in each case, there is the factor of 2 & x that is shared by both. These are what is used to find the Greatest Common Factor. Multiply both terms together:

2 * x = 2x

2x is your GCF.

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