Question

In how many ways the number $18900$ can be split in two factors which are relative prime (or coprime).

Answer 1

Here $N=18900=2^2{.3}^3{.5}^2{.7}^1$
Co-prime means consecutive primes. Here co-primes are $2,3,5,7.$
$\therefore n=4\left(\text{number of different factor in N}\right)$
Hence number of ways in which a composite numbers $N$ can be resolved into two factors which are relative prime (or co-prime)
$=2^{4-1}=2^3=8$