A number theory problem by Gajender Singh

$P={ A }^{ N }\times { L }^{ M }......\infty \\ SO\quad NO.\quad OF\quad FACTOR=\left[ N+1 \right] \left[ M+1 \right] ..........\infty \\ IF\quad P=2400\\ THEN\quad 2400={ 2 }^{ 5 }\times { 3 }^{ 1 }\times { 5 }^{ 2 }\quad \\ SO\quad NO.\quad OF\quad FACTOR=[5+1][1+1][2+1]\\ =6*2*3=\bigstar 36\bigstar$