php recursion error factoring

Question

so I am new at the idea of recursion and i wrote this simple code to factor a number ($n) this is the code:

$n = 120;
$y = 1;

function factor($n, $y) {
    if($y > $n) {
        return 1;
    } else {
        $x = $n / $y;
        list($whole, $dec) = array_pad(explode('.', $x), 2, Null);
        if($dec == '') {
            echo 'x:' . $x . ' y:' . $y . '</br>';
            return factor($n, ($y + 1));
        }
    }
}

this is what the code outputs:

x:120 y:1
x:60 y:2
x:40 y:3
x:30 y:4
x:24 y:5
x:20 y:6

so my question is why does this stop before it completes?

Answer 1

Your next step would be 120 / 7 which equals 17.142857....

So this check fails and as such the recursion does not happen:

if($dec=='') // $dec would equal to 142857.....
{
    echo'x:'.$x.' y:'.$y.'</br>';
    return factor($n,($y+1));
}

Answer 2

else
{
    $x=$n/$y;
    list($whole,$dec)=array_pad(explode('.', number_format($x)), 2, Null);
    if($dec=='')
    {
        echo'x:'.$x.' y:'.$y.'</br>';
        return factor($n,($y+1));
    }
}

PART OF DECIMAL LIMITATION

Answer 3

There are two things I see wrong with your example:

1. Your recursion stops the first time it encounters a fractional value. The tail recursion (return factor($n, $y + 1);) only occurs when $dec == ''. Otherwise, the function simply exits. That's why it stops when $y is 7.
2. Your condition for ending recursion ($y > $n) is incorrect. You want to break the recursion when the divisor is greater than the quotient — i.e., when $y > $x — because that means you've found all the integer factors.

I think this is what you want:

$n = 120;
$y = 1;

function factor($n, $y) {
    $x = $n / $y;

    if($y > $x) {
        return 1;
    } else {
        list($whole, $dec) = array_pad(explode('.', $x), 2, Null);

        if($dec == '') {
            echo 'x:' . $x . ' y:' . $y . "</br>\n";
        }

        return factor($n, ($y + 1));
    }
}

echo factor($n, $y);