How many factors of $N$ are a multiple of $K$? How many factors of $N = 12^{12} \times 14^{14} \times 15^{15}$ are a multiple of $K = 12^{10} \times 14^{10} \times 15^{10}$ ?

Any approach to attempt such questions ?

Hint:
Since $\;N=2^{38}\cdot3^{27}\cdot5^{15}\cdot7^{14}\;,\;\;K=2^{30}\cdot3^{20}\cdot5^{10}\cdot7^{10}\;$
You need that each multiple has at least the same ammount of prime factors as $\;K\;$ has...
