# What is the greatest common factor of #51x^3y^2 - 27xy + 69y#?

##### 2 Answers

3y

#### Explanation:

I did this in two steps. I first looked at the numeric coefficients to determine if there was a common factor for the polynomial:

51 -27 69

51 is divisible by 3 and 17

27 is divisible by 3 and 9, and 9 is

69 is divisible by 3 and 23

since the shared factor among the three coefficients is 3, we can pull that out of the whole equation as a common factor:

Next, we can see if there are non-numeric coefficients (x and y in this case) that are used in all 3 terms. x is used twice, but y is found in all three terms. This means we can pull y out of the equation. You do this by dividing all 3 terms by y and putting a y outside the parentheses:

The greatest common factor is the value outside of the parentheses in the above equation, meaing your answer is

#### Explanation:

Find the GCF of the constants and the composite variables separately:

Combining the factors: