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

Let $N=18900=2^2\cdot 3^3\cdot 5^2\cdot 7^1$

Relatively prime or coprime Two numbers not necessarily prime are said to be relatively prime or coprime, if their $HCF$ (highest common factor) is one as $2, 3, 5, 7$are relatively prime numbers. 

$\therefore n=4$ [number of different primes in $N$] 

Hence, number of ways in which a composite number $N$ can be resolved into two factors which are relatively prime or coprirne $=2^{4-1}=2^3=8$