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.

Question

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?
A.Gary did not use correct factors for 66 in the equation.
B.Gary did not use correct factors for 36 in the equation.
C.Gary did not use two equivalent expressions in the equation.
D.Gary did not use the greatest common factor in the equation.

Answer 1

The statement that best describes Gary’s error is:

D. Gary did not use the greatest common factor in the equation.

The greatest common factor of 66 and 36 is actually 6, and he incorrectly factored out 3 instead. The correct factorization using the greatest common factor would be:

66 + 36 = 6(11 + 6)

Therefore, option D accurately identifies his mistake.