Question

How do you list all the factorials up to 20?

Answer 1

As we know that factorial is a function which is denoted by $n!$ for any integer $n$ and is the product of all positive integers less than or equal to $n$. So we will use the definition of factorial to find the factorial of the first 20 numbers.

Complete step by step answer:
We have to find the factorials up to 20.
Now, we know that factorial is the product of all positive integers less than or equal to the given number. Factorials are used in the permutations and combinations. Factorials are also used to solve the algebra and calculus, finding probability, used as the coefficients of terms of binomial theorem. Factorial is also used to find the number of way n objects can be arranged. A factorial for integer $n$ is denoted by $n!$ and is defined by
$n!=n\times \left( n-1 \right)!......3\times 2\times 1$ for $n>0$.
Now, we have to list all the factorials up to 20.
So let us start with 1 and go ahead we will get
$\begin{aligned} & 1!=1 \\\ & 2!=2\times 1=2 \\\ \end{aligned}$
$\begin{aligned} & 3!=3\times 2\times 1=6 \\\ & 4!=4\times 3\times 2\times 1=24 \\\ & 5!=5\times 4\times 3\times 2\times 1=120 \\\ & 6!=6\times 5\times 4\times 3\times 2\times 1=720 \\\ & 7!=7\times 6\times 5\times 4\times 3\times 2\times 1=5040 \\\ & 8!=8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=40320 \\\ & 9!=9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=362880 \\\ & 10!=10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=3628800 \\\ & 11!=11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=39916800 \\\ & 12!=12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=479001600 \\\ & 13!=13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=6227020800 \\\ & 14!=14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=87178291200 \\\ & 15!=15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=1307674368000 \\\ & 16!=16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=20922789888000 \\\ & 17!=17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=355687428096000 \\\ & 18!=18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=6402373705728000 \\\ & 19!=19\times 18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=121645100408832000 \\\ & 20!=20\times 19\times 18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1=2432902008176640000 \\\ \end{aligned}$
So above is the list of factorials upto 20.

Note: The points to be noted are that factorials are always integers. The value of $0!$ is always one. As the multiplication is quite lengthy so be careful and avoid calculation mistakes. It is not easy to remember the values of factorials so try to remember the concept and solve any factorial by using the concept step by step.