Question

Pairs of numbers that are bigger than 17

Answer 1

x = 17*a

y = 17*b

such that HFC(a,b)=1 (because x,y have no common factor bigger than 17)

We also know that x+y=187

Hence, a+b = 187 / 17 = 11

Therefore, assuming a reasonable (but not specified in your question) constraint that x,y are positive, (a,b) may be (1,10), (2,9),(3,8),(4,7),(5,6).

All of these pairs are co-prime (having HFC equal to 1), hence their HCF is 17 like you requested.

Hence there are 5 possible pairs of integers (x,y) that satisfy your restrictions (and you can also switch the roles of x and y to have 10 pairs, if order does NOT matter)

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