I can start by listing the multiples of 7 in that range: 49, 56, 63. 49 is too low and 63 is too high, so 56 is the only possible candidate. To check, I can divide 56 by 7 and get 8, which has no common factors with 21 except 1. Therefore, 56 is the number I'm looking for. 
The greatest common divisor of 21 and some number between 50 and 60 is 7. What is the number?