我提供一个吧。。。。

    $int = 111;
    
    if(!is_int($int) || $int === 0) {
        echo "wrong number!";die;    
    }
    
    if($int <= 2) {
        echo $int . "=" . $int;die;
    }
    
    $result = $int . '=';
    while($int%2 == 0) {
        $int     = $int/2;
        $result .= 2 . '*';
    }
    
    for($i = 3; $i <= $int; $i += 2) {
        while($int%$i == 0) {
            $int     = $int/$i;
            $result .= $i . '*';
        }
    }
    
    $result = trim($result, '*');
    
    echo $result;die;

先对数字进行因式分解算法
再过滤结果集中，不符合的结果集。

class Helper
{
    public function chechPrime($num)
    {
        for ($i = floor(sqrt($num)); $i > 1; --$i) {
            if ($num % $i == 0) {
                return false;
            }
        }
        return true;
    }

    public function getFactorNumber(array &$result, array &$list, $n, $startFactor)
    {
        if ($n == 1) {
            if (count($list) > 1) {
                $result[] = $list;
            }
            return;
        }

        for ($i = $startFactor; $i <= floor(sqrt($n)); ++$i) {
            if ($n % $i === 0) {
                array_push($list, $i);
                $this->getFactorNumber($result, $list, $n / $i, $i);
                array_pop($list);
            }
        }

        array_push($list, $n);
        $this->getFactorNumber($result, $list, 1, $n);
        array_pop($list);
    }

    public function primeFactorNumber($num): array
    {
        $result = [];
        $list = [];

        $this->getFactorNumber($result, $list, $num, 2);
        array_push($result, [$num, 1]);

        $result = array_filter($result, function ($value) {
            foreach ($value as $v) {
                if (!$this->chechPrime($v)) {
                    return false;
                }
            }
            return true;
        });

        return $result;
    }
}

$helper = new Helper();

$result = $helper->primeFactorNumber(90);

var_dump($result);