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If the (n+1) numbers a, b, c, d, \ldots, be all different and each of them a prime number, then the number of different factors (other than 1 ) of a^m \cdot b \cdot c \cdot d \ldots is

Option: 1

m-2^n


Option: 2

(m+1) 2^n


Option: 3

(m+1) 2^n-1


Option: 4

none of these


Answers (1)

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Number of different factors of a^m \cdot b \cdot c \cdot d \ldots
                        \begin{aligned} & =(m+1)\{(1+1)(1+1)(1+1) \ldots n \text { factors }\}-1 \\ & =(m+1) 2^n-1 \end{aligned}

 

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