Greatest common factor of 14 and 35?

Answer 1

Let's find out using the Euclidean method! Divide 35 by 14 and you get 2, remainder 7. Divide 14 (the divisor in the last division problem) by 7 (the last remainder) and you get 2, remainder 0. Because the remainder is zero, the last divisor, 7, is the GCF of 14 and 35. Check. Seven is definitely a factor of both, and if we were to try larger numbers, they would not work: 14 does go into 14, but not into 35; and no number larger than 14 goes into 14.
The GCF is 7.