N is a natural number. 2N is having 28 factors, 3N is having 30 factors. How many factors 6N will have. options 36, 35, 32, 40, non of these.

Question

Answer 1

Since 2N and 3N have different number of factors, so number N must have 2's in it. On factorising 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. Option B

Answer 2

Since 2N and 3N have different number of factors, so number N must have 2's in it. On factorising 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. Option B

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N is a natural number. 2N is having 28 factors, 3N is having 30 factors. How many factors 6N will have. options 36, 35, 32, 40, non of these.