Question 13
The sum of two natural numbers is $$150$$. Their HCF is $$15$$. The number of pairs of such numbers is
Solution
Write the numbers as $$15x$$ and $$15y$$, where $$\gcd(x,y)=1$$. Then $$x+y=10$$. The coprime unordered pairs are $$(1,9)$$ and $$(3,7)$$, so there are $$2$$ pairs.
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