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

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.