N isa number, such that 2n has 28 factors and 3n has 30 factors. Then 6n has how many factors

Question

Answer 1

Hi Pradeep,
Since 2N and 3N have different number of factors, number N must have 2's in it. On factorizing of 28 (14*2, 7*4, 28*1) we can observe that N must be 2^5*3^3.
So 6N would be 2^6*3^4 . Hence the number of factors will be 7*5 = 35.

Answer 2

Hi Pradeep,
Since 2N and 3N have different number of factors, number N must have 2's in it. On factorizing of 28 (14*2, 7*4, 28*1) we can observe that N must be 2^5*3^3.
So 6N would be 2^6*3^4 . Hence the number of factors will be 7*5 = 35.

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N isa number, such that 2n has 28 factors and 3n has 30 factors. Then 6n has how many factors