Question

What is 26!?

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 26 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 solution:
Here we are provided with the expression 26! 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: - $6!=6\times 5\times 4\times 3\times 2\times 1=720$.
Let us come to the question. We have to find the factorial of 26, so using the above formula we get,
$\Rightarrow 26!=26\times 25\times 24\times 23\times ....\times 1$
On performing the above multiplications in a scientific calculator we get,
$\Rightarrow 26!=4.03291461\times {{10}^{26}}$
Hence, the above expression is our answer.

Note: Here, we will be required to use the scientific calculator for calculation of the product of the first 26 natural numbers as it will take much time if we will try to calculate on paper. You can see that ${{10}^{26}}$ will be a huge number. Factorials are important in the chapter permutation and combination where we have to select r things out of a total of n things.