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Question

Let S be the set of all ordered pairs (x,y) of positive integers, with HCF(x, y)=16 and LCM(x, y)=48000. The number of elements in S is?

A
4
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B
8
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C
16
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D
32
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Solution

The correct option is B 8
let numbers are x=16×a and y=16×b, where a and b are co-prime numbers.
and L.C.M(x,y)=16×a×b=16ab=48000ab=3000
factors of 3000=2×2×2×3×5×5×5
possible values of ab=1×3000,3×1000,8×375, and 24×125
Thus, number of elements in S=8.

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