while循环中的模数如何执行？

Question

I need help understanding this solution for getting a prime factor. this is the code demo

function getMaxPrimeFactor (n) {
    var temp = n;
    for(var i = 2; i < temp; i++) {
        while (temp % i === 0) {
            temp /= i;
        }
    }   
    console.log(temp);
}

getMaxPrimeFactor(13195);

I understand the for loop but I don't know what's going on the while loop and the division, how did it get an output of 29?

Answer 1

Here's what is going on:

The point of the for loop is to try every single divisor between 2 and the current value of temp which starts out equal to the original number.

The point of the while loop is to take each one of those divisors and try them as many times as possible. As long as the remainder comes up 0 meaning it divided evenly, then keep dividing and reduce temp to the result of the division each time.

So, while (temp % i === 0) means to keep running the while loop as long as temp divides by i evenly with no remainder. The % modulus operator computes the remainder after division.

Here's a more instrumented version that when you run it shows you a bit more about what is going on:

 function getMaxPrimeFactor (n) { var temp = n; for(var i = 2; i < temp; i++) { while (temp % i === 0) { temp /= i; console.log("factor=",i,", ",temp*i,"/",i, "=",temp); } } console.log("remaining factor=",temp); } getMaxPrimeFactor(13195); 

Answer 2

Here while is checking if value of temp % i is 0 (ie if temp is divisible with i ). If this condition is true it will store temp / i in temp

So when the while condition is true

i   temp   (temp % i)  new_temp_value(temp/i)
5   13195  0           2639
7   2639   0           377
13  377    0           29
29  29     -           - //for loop stops here since `i < temp` condition doesn't satisfy.

Last temp value is 29

So if we consider only i value from above, we get 5, 7, 13, 29 which are factors of 13195 .

ie 5 * 7 * 13 * 29 = 13195

So the max value in factors is 29 .