What is the greatest common factor of 210 and 252?

Answer 1

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, and 252.
The greatest common factor is 42.

These are large enough numbers with enough factors that finding the prime factors of each is likely to be easier than determining all the factors.
The prime factors of 210 are 2, 3, 5, and 7.
The prime factors of 252 are 2, 2, 3, 3, and 7.
The common factors are one 2, one 3, and 7, so the greatest common factor is 2 x 3 x 7 = 42.

THE ANSWER IS 42!