Question

How many natural numbers are factors of exactly one of the numbers 675 and 1080?

Answer 1

`5040 = 2^(4) xx 3^(2) xx 5^(2) xx 7^(1)`
No. of factors `= (4+1) (2+1) (1+1) (1+1)`
`= 5 xx 3 xx 2 xx 2 = 60`
If 1 and 5040 are not the factors then Remaining factors `= 60 - 2 = 58`.