Question

Factorial of negative number is always greater than 1.
A. True
B. False
C. Either
D. Neither

Answer 1

Hint: Factorial of a number is equal to the product of all consecutive integers less than or equal to the given number.

Complete step-by-step solution -
Factorial in particular understanding can be explained as the number of ways to permute or arrange the objects.
Example: Factorial of \[5\] is written as:
\[5!=5\times 4\times 3\times 2\times 1=120\]
This can also be explained the number of ways \[5\] objects, say \[5\] books can be arranged
i.e. \[5\times 4\times 3\times 2\times 1=120\] ways.
So the factorial of a non negative number is always greater than \[1\].
In this respect, the factorial for negative numbers does not exist because we cannot permute or arrange objects which are less than zero.
Hence the factorial of negative numbers can never be greater than. Answer is false.

Note: In general a number of things cannot be negative. That’s why we can say that we can never define the factorial of a negative number. Also factorial of 0 is 1.