Question

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

Answer 1

28 = 4*7
2n = 2^6*3^3 ---. n = 2*2^5*3^3
30 = 5*6
3n = 2^5*3^4 --> n = 3*2^5*3^3
6n = 2^6*3^4
total factors of 6n = 7*5 = 35

Answer 2

28 has factors->28*1,14*2,7*4
30 has factors ->30*1,3*10,3*2*6,6*5
why did u choose only 7*4 and 6*5