Question

Evaluate 7!?

Answer 1

Hint: First we will understand about the term factorial of a number. Now, to find the factorial of the given number we will start with 7 and then keep on decreasing the numbers with 1 unit till we reach the number 1. We will take the product of all these natural numbers to get the answer. Use the formula $n!=n\left( n-1 \right)\left( n-2 \right)\left( n-3 \right).....1$ where n is a non negative integer.

Complete step by step answer:
Here we are provided with the expression 7! And we are asked to find its value. First we need to understand the term ‘factorial’ of a number.
Now, in mathematics the factorial of a non negative integer ‘n’ is the product of all the positive integers that are smaller than n and including n. It is denoted as $n!$ and its expression is given as $n!=n\left( n-1 \right)\left( n-2 \right)\left( n-3 \right).....1$. The value of n cannot be fraction, decimal, negative integers etc. because there is no meaning of the factorial of such numbers. For example: $5!=5\times 4\times 3\times 2\times 1=120$.
Let us come to the question. We have to find the factorial of 7, so using the above formula we get,
$\Rightarrow 7!=7\times 6\times 5\times 4\times 3\times 2\times 1$
On performing the above multiplication of first seven natural numbers we get,
$\Rightarrow 7!=5040$

Hence, the value of the factorial of 7 is 5040.

Note: Note that sometimes we will be required to use the scientific calculator for calculation of product of the natural numbers because the number whose factorial is to be found will be large as it will take much time if we will try to calculate on paper. In such cases we use the scientific notation to write the answer. Factorials are important in the chapter ‘permutation and combination’ where we have to select r things out of a total of n things.