3-digit numbers with a product of own digits

Number Theory Level 3

Find the sum of all 3-digit numbers a b c ‾ \overline{abc} such that

a b c ‾ = a b c ( a + b + c ) . \overline{abc}=abc(a+b+c).

If you think there are no such numbers, submit − 1 -1 as the answer.


The answer is 279.

Khang Nguyen Thanh by Khang Nguyen Thanh , 27, Vietnam

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1 solution

Kyle T
May 7, 2019

using the code below, we can find the two numbers that satisfy this condition are 135 and 144, the sum of which is our answer, 279. 

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<?php
$numbers = array();
for($i=100;$i<=999;$i++){
    $arr = str_split($i);
    if(array_product($arr)*array_sum($arr)==$i){
        $numbers[] = $i;
    }
}
echo (count($numbers)) ? array_sum($numbers) : '-1';
?>

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