n is a number such that 2n has 28 factors and 3n has 30 factors,then 6n has how many factors

Hi Neha,

here,

for 2n, 28 = 7*4

for 3n,30= 6*5 

Hence, one factor of n should be 2 raised to the power of 5.

 the other factor is 3 raised to the power of  3.

When n is multiplied by 6

Number of factors of 6n = 7*5 = 35

Thanks,

Varun.