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Question

Let A={(a,b,c):a,b,cN, a(bc)=64}, then the total number of ordered triplets is

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Solution

a(bc)=64
64=26=43=82=641

If a=2, then bc=6
b=2, c=3;
b=3, c=2;
b=1, c=6;
b=6, c=1

If a=4, then bc=3
b=1, c=3;
b=3, c=1

If a=8, then bc=2
b=1, c=2;
b=2, c=1

If a=64, then bc=1
b=1, c=1

Total number of ordered triplets =4+2+2+1=9

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