Question

Find the number of ways in which the number $300300$ can be split into $2$ factors which are relatively prime

Answer 1

Let $N=300300=2^2\times 3^1\times 5^2\times 7^2\times {11}^1\times {13}^1$
Thus number of different prime factor in $N$ is $=6$
Hence number of ways in which $N$ can be split into two factor
which are relatively primes is $2^{6-1}=2^5=32$