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A positive integer `n` is of the form `n=2^(alpha)3^(beta)`, where `alpha ge 1`, `beta ge 1`. If `n` has `12` positive divisors and `2n` has `15` positive divisors, then the number of positive divisors of `3n ` isA. `15`B. `16`C. `18`D. `20` |
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Answer» Correct Answer - B `(b)` `n=2^(alpha)*3^(beta)` No. of divisors `=(alpha+1)(beta+1)=12` `2n=2^(alpha+1)3^(beta)` No.of divisors `=(alpha+2)(beta+1)=15` `implies(alpha+2)/(alpha+1)=(5)/(4)` `implies4alpha+8=5alpha+5impliesalpha=3` `impliesbeta=2implies3n=2^(3)3^(3)` No. of divisors `=(3+1)(3+1)=16` |
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