During our college days, we used to run various programs, some of them we used to understand and some of them we used to mug up. Once again i have thought to recall those programs and try to explain as simple as possible so that I can brainstorm myself and any students who go through it can easily get the logic behind it.

First of all, let us understand what is factorial of a number,

The factorial of a non-negative integer n is denoted by n! is the product of all positive integers less than or equal to n. example

Factorial of 4! = 1 * 2 * 3 *4 = 24

Factorial of 5! = 1 * 2 *3 * 4 * 5 = 120

n! = n*(n-1)*(n-2)*(n-3)…3.2.1

<?php
$num=4;
$fact=1;
for($i=1;$i<=$num; $i++){
$fact=$i*$fact;
}
echo "factorial of a number ".$num is $fact;

In the above code, i am trying to find the factorial of a number 4, whereas I have initialized $fact variable with 1 as shown above, as we start our product of a number with 1.

Factorial of 4! = 1 * 2 * 3 *4 = 24

we are going to start from 1 and continue multiplying the number we have, ie. 4 so we are going to make use of for loop.

Now let us consider our looping. here we initialize variable $i with 1 and compare if it is less or equal to the number, so the first condition is correct (1<=4), so we go inside loop and execute the statement.

$fact= 1* 1 ($fact value that has been initialized)

$fact=1

now variable $i is incremented with one as we have $i++ in our loop so the new value of $i is $i=1+1=2;

now we will check the condition (2<=4), even this condition is correct so we execute the statement

$fact= $i*$fact

$fact= 2*1;($fact=1 which is previous value of $fact that we obtained after executing the statement)

$fact=2

Again $i is incremented by 1 and has become 2+1 =3, and we check condition (3<=4) which is again correct, so our statement becomes

$fact= $i*$fact

$fact= 3*2;($fact=2 which is previous value of $fact that we obtained after executing the statement)

$fact=6

Again $i is incremented by 1 and has become 3+1 =4, and we check condition (4<=4) which is again correct, so our statment becomes

$fact= $i*$fact

$fact= 4*6;($fact=6 which is previous value of $fact that we obtained after executing the statement)

$fact=24

Again $i is incremented by 1 and has become 4+1 =5, and we check condition (5<=4) which is false, so we come out of the loop and print the final factorial value.

So the final factorial value of 4 is 24

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