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The greatest integer which divides (p+1)...

The greatest integer which divides `(p+1)(p+2)(p+3)…(p+q)` for all `p in N` and fixed `q in N` is

A

`p!`

B

`q!`

C

p

D

q

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Let p be a prime number and n be a positive integer then exponent of p in n! is denoted by ^E_p(n! ) and is given by E_p(n!)=[n/p]+[n/(p)^2]+[n/(p)^3]+....[n/(p^k)] where p^kltnltp^(k+1) and [x] denotes the greatest integral part of x if we isolate the power of each prime contained in any number N then N can be written as N=2^(alpha_1).3^(alpha_2).5^(alpha_3).7^(alpha_4) ....where alpha_i are whole numbers The number of zeros at the end of 108! is

The properties (p to ~q)^^(~ p to p) is a

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