Question

Gary applied the distributive property using the greatest common factor to determine the expression that is equivalent to 66 + 36. His work is shown below.

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

66 + 36 = 3(22 + 12)

What statement best describes Gary’s error?

Answer 1

Answer: Gary has made mistake in taking the greatest common factor i.e.

he takes 3 instead of 6.

Explanation:

Since we have given that

`66+36=3(22+12)`

He has made mistake.

As he wants to apply the greatest common factor to determine the expression.

But we can see that there is greatest common factor is '6'.

So, using distributive property:

6(11+6)

Gary has made mistake in taking the greatest common factor i.e.

he takes 3 instead of 6.

Answer 2

Gary did not use the Greatest Common Factor when he factored it out. The GCF should have been 6 instead of 3, so it should be 66+36=6(11+6).