I was browsing through my subscribed threads for problems that were never completely dealt with. This is one such thread that I'd like to understand. In response to Random's answer (or anyone else reading this), both my book and my previous instructor encouraged the use of calculators for checking answers, but discouraged their use for solving problems. I agree with the idea of not allowing the calculator to do any of my work for me (at this point in time).

By "the pair," I suppose you're referring to

And not

Since 4,753 is a prime number.

Given the restraint of solving by hand, I'm having difficulty determining how I might ascertain the pair's Highest Common Factor... especially if this is the only method available for simplifying this fraction in particular.