Question

How to evaluate the expression 8!?

Answer 1

Hint: This is a simple mathematical problem. To solve this we need to know just multiplication. Here we will multiply all the numbers from 1 to the given number to which we need to find the factorial. So by multiplying all those numbers we will get the answers.

Complete step by step answer:
Factorial is the product all the positive integers until the given number.so factorial of a number n can be given by
\[n!=n\times \left( n-1 \right)\times \left( n-2 \right)\times .......1\]
Factorial can also be written in pi production notation.
\[n!=\prod\limits_{i=1}^{n}{i}\]
From the above formulas, the recurrence relation for the factorial of a number is defined as the product of factorial number and factorial of that number minus 1. It is given by:
\[n!=n\times \left( n-1 \right)!\]
Factorial can also be calculated as division of factorial of n+1 and n+1. The quotient is the factorial of number n. The formula is
\[n!=\dfrac{\left( n+1 \right)!}{\left( n+1 \right)}\]
The factorial operation is encountered in many areas of Mathematics such as algebra, permutation and combination, and mathematical analysis. Its primary use is to count n possible distinct objects.
 So we can find the product of all the positive integers less than that number.
In our question n is 8
So we have to calculate factorial of \[8!\]
According to the formula the factorial of \[8!\] is calculated as
\[8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\]
Now calculating the factorial
\[\Rightarrow 56\times 30\times 12\times 2\]
\[\Rightarrow 56\times 30\times 24\]
\[\Rightarrow 56\times 720\]
\[\Rightarrow 40320\]

So the value of factorial of 8 is \[40320\].

Note: The factorial of 0 is 1. According to the convention of empty product, the result of multiplying no factors is a nullary product. It means that the convention is equal to the multiplicative identity. Also the factorial of negative numbers does not exist.