jmc

The prime factorization of 84 is $2^2\times 3\times 7$, the prime factorization of 112 is $2^4\times 7$, and the prime factorization of 210 is $2\times 3\times 5\times 7$. The greatest common factor of the three numbers is the product of all the prime factors that they have in common, which is $2\times 7=\boxed{14}.$