Why is 3 the gcf of 12 and 33?

Answer 1

3*4 = 12

3*11 = 33

so 3 is a factor of both 12 and 33. That is 3 is a common factor.

No number larger than 3 is a factor of BOTH the numbers so 3 is the greatest common factor.

Answer 2

Because 3 is the largest positive integer that divides evenly into both 12 and 33 with no remainder.