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If P(1), P(2), P(3), ……, P(m+1) are di...

If ` P_(1), P_(2), P_(3), ……, P_(m+1) ` are distinct prime numbers. Then the number of factors of `P_(1)^(n) P_(2)P_(3)...... P_(m+1)` is :

A

`m(n+1)`

B

`2^(n)m`

C

`(n+1)2^(m)`

D

`n.2^(m)`

Text Solution

Verified by Experts

The total number of factors of `x^(n)yz......` is equal to the number of ways of selecting one or more out of in identical quantities of one type and remaining m distinct quantities.
Hence, the required number of factors `=(n+1)2^(m)`.
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