Question 113

If x and y are two positive integers, and m is the HCF of x and y such that mxy = 1080 and 3 < m < 12 , then how many possible ordered pairs of x and y exist?

Solution

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Factorize 1080 - $$2^3\cdot3^3\cdot5$$. Here, HCF has to be between 3 and 12; the only possible number would be 6. The remaining thing that exists is only 5. So there are two ways: one, 5, belong to x, and two, five, belong to y.

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