Question

Find the number of ways in which the number 300300 can be split into two factors which are relatively prime.

Answer 1

`300300=2^(2)xx3^(1)xx5^(2)xx7^(1)xx11^(1)xx13^(1)`
Now we have to make factors which are relative prime.
Each of `2^(2),3^(1),5^(2),7^(1),11^(1),13^(1)` should be considered single factor.
So number of divisors =(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)
`=2^(6)=64`
Number of ways of splitting into 2 factors`=(64)/(2)=32`