Introduction
Category : JEE Main & Advanced
(1) The Factorial : Factorial notation: Let \[n\] be a positive integer. Then, the continued product of first \[n\] natural numbers is called factorial n, to be denoted by \[n\,!\] or \[\left| \!{ {\,n \,}} \right. \].
Also, we define \[0!=1\].
when \[n\] is negative or a fraction, \[n\,\,!\] is not defined.
Thus, \[n\,\,!=n(n-1)\,(n-2)\,....\,3.2.1.\]
(2) Exponent of Prime \[p\] in \[n\,!\] : Let \[p\] be a prime number and \[n\] be a positive integer. Then the last integer amongst 1, 2, 3, ....... \[(n-1),\,\,n\] which is divisible by \[p\] is \[\left[ \frac{n}{p} \right]p\], where \[\left[ \frac{n}{p} \right]\] denotes the greatest integer less than or equal to \[\frac{n}{p}\].
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