custom-factorial.php

<?php
/**
 * Usage:
 *      ms(12345, 3) # returns "37035"
 *      ms(999, 3) # returns "2997"
 *      ms("1111", 24) # returns "26664"
 *
 * @param   int|stirng  $s  A string containing a positive integer
 * @param   int         $m  The multiplier
 * @return  string          The product of the multiplication (as a string)
 */
function ms($s, $m) {
    $l = str_split($s);

    $cs = 0;
    $r = array_reduce(array_reverse($l), function ($c, $x) use ($m, &$cs) {
        $p = $x * $m + $cs;
        if ($p > 9) {
            $cs = substr($p, 0, -1); // tens
            $p = substr($p, -1);
        } else {
            $cs = 0;
        }

        return $p . $c;
    }, "");
    if ($cs) $r = $cs . $r;

    return $r;
}

function fac($n) {
    $x = 1;
    for ($i = $n; $i > 1; $i--) {
        $x = ms((string) $x, $i);
    }
    return $x;
}



var_dump("fac(13)",     $s = fac(13),   $s === "6227020800");
var_dump("fac(100)",    $s = fac(100),  $s === "93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000");