jmc

Produce an exhaustive list of the pairs of factors which multiply to give 60, as well as the sum and the difference of each pair of factors. $$\begin{array}{ccc}Factors& Sum& Difference\\ (1,60)& 61& 59\\ (2,30)& 32& 28\\ (3,20)& 23& 17\\ (4,15)& 19& 11\\ (5,12)& 17& 7\\ (6,10)& 16& 4\end{array}$$ The only number which appears in both the second column and the third column is 17. Therefore, $(A,B)=(20,3)$ and $(C,D)=(5,12)\text{ or }(12,5)$. In particular, $A=\boxed{20}$.