If $x,y_1,y_2\mathrm{.....}{y}_m$  are (m + 1) distinct prime numbers, the number of factors of $x^n\times y_1\times y_2\times \mathrm{.....}\times y_m$$(n\in N)$   is

The total numbers of factors of $x^{n}yz$ …. is equal to the number of ways of selecting one or more out of n identical quantities of one type and remaining m distinct quantities. Hence, the required numbers of factors = $\left(n+1\right)2^m$