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Q.

If  p,q,r,s,t be distinct primes and  N=pq2r2st, then which of the following is/are not TRUE?

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a

N can be written as a product of two positive integers in atmost 72 ways (Order doesn’t matter)

b

N cannot be divisible by 13!

c

N can be written as a product of two positive integers in atmost 48 ways (Order doesn’t matter)

d

N has 96 positive divisors 

answer is A.

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Detailed Solution

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Number of divisors  =(1+1)(2+1)(2+1)(1+1)(1+1)=72
 Since there are 6 primes which are  13 and N contain only five distinct primes, N cannot be divisible by 13!.
 

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If  p,q,r,s,t be distinct primes and  N=pq2r2st, then which of the following is/are not TRUE?