Why Is This Factorial Algorithm Not Accurate

Question

Sorry I feel stupid asking this and am prepared to lose half of my points asking this but why does this algorithm not work? It works up to a point. After the number 13 the factorials are a little off. For instance the numbers do not entirely match in the hundreds thousands place and onward.

#include <stdio.h>

float factorial(unsigned int i) {

    if (i <= 1) {
        return 1;
    }
    return i * factorial(i - 1);
}

int  main() {
    int i = 13;
    printf("Factorial of %d is %f\n", i, factorial(i));
    return 0;
}

Here's the output:

Factorial of 13 is 6227020800.000000

Here is an example of inaccurate output:

Factorial of 14 is 87178289152.000000

The output for the number 14 should actually be this (from mathisfun.com)

14        87,178,291,200

I changed the return type to float to obtain more accurate output but I obtained this code for the most part from here: https://www.tutorialspoint.com/cprogramming/c_recursion.htm

EDIT: If I change to the return type to double the output is accurate up to 21.I am using the %Lf string formatter for the output in the printf function.

Answer 1

Simple. float cannot accurately store integers above 16777216 without loss of precision.

int is better than float. But try long long so you can properly store 19 digits.