最大公因数解说明

Question

Have the function Division(num1,num2) take both parameters being passed and return the greatest common factor. That is, return the greatest number that evenly goes into both numbers with no remainder. For example: 12 and 16 both are divisible by 1, 2, and 4 so the output should be 4. The range for both parameters will be from 1 to 10^3. Can anyone please explain the solution here?

function Division(num1, num2) { 
    var largestFactor = 1; 
    var smallerNum; 

    if (num1 > num2) { 
        smallerNum = num2; 
    } else { 
        smallerNum = num1; 
    }          

    for (i = 1; i <= smallerNum; i++) { 
        if ((num1 % i === 0) && (num2 % i === 0) && (i > largestFactor)) { 
            largestFactor = i; 
        } 
    } 
    return largestFactor; 
} 

• Why set a new variable = 1?
• Why set second variable?
• Why is it that with num1 > num2 , we get num2=smallerNum , and vice versa?
• And explain why i <= smallerNum if i > largestfactor ?

Answer 1

why set aa new variable = 1?

It's a default value, so it can compare it to the counter. All numbers different from 0 have a common denominator of 1. Since you want the variable to be used only within the context of the function and not create a global variable, you define the variable outside the loop. You didn't need to set it up to 1, because your loop already covers that, but you'll need to get rid of that pointless comparison (look at the bottom of this answer).

why set second variable?

There can't be a larger common denominator that is larger than one of the numbers. Hence, you should only check numbers until you reach the smallest one.

why if num1>num2 , num2=smallerNum, vice versa?

If num1 is bigger than num2, num2 is the smaller one. Viceversa, if num2 is bigger than num1, num1 is the smaller one.

and if please explain this part...why i<=smallerNum and if i > largestfactor?

The loop goes from 1 to the smallest number. i <= smallerNum says.. while i is smaller or equal than smallerNum keep running.

i > largestfactor is comparing the last known largest factor to the new one. Kind of pointless to be honest (it will always return true, except for the first iteration because 1 is not bigger than 1).

Answer 2

It sets largestFactor to be 1 because 1 is the minimum GCF for any two numbers greater than 0 and largestFactor is increased later on to get the actual GCF.

smallerNum is technically not needed for the functionality, but it'd increase performance by setting it and using it in the loop rather than calculating it on each iteration. It does not change.

If num1>num2 , num2 is smaller, so we use smallerNum = num2 to set smallerNum to be equal to num2 . Note that this is very different from num2 = smallerNum as that sets num2 to be equal to smallerNum , changing the value of num2 rather than smallerNum . Order of the values when using the assignment operator = is very important. The same logic applies when num2>num1 , which is the purpose of the else.

As the factors of a number is always less than or equal to the number, the GCF of the two numbers is always going to be less than or equal to the smaller number. This is why we calculate the smaller number in the beginning. The i<=smallerNum tells the loop to keep running as long as i is less than or equal to smallerNum and stop once that is no longer true. This is needed to make sure we don't increase i infinitely and since any number larger than the smaller number is irrelevant, we can stop once i is equal to smallerNum .

i > largestFactor compares if the current number being tested is larger than the previous found factor. This isn't needed and can be removed since our loop only goes up. Having this extra calculation would only slow down the program.

Answer 3

I hope to solve your problem

  for($i = $num1; $i > 0; $i --){
    if ($num1%$i == 0 && $num2%$i == 0){
      return $i;
    }
  }