## Question

The number of positive integers *n* such that 2* ^{n}* divides

*n*! is

### Solution

None of these

The exponent of 2 in *n*! is given by

where [*x*] is denotes greatest integer after finite number of terms. Thus we get

Thus, there is no positive for which integer for which 2* ^{n}* divides n!

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