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iOS

Posted by Brandon D'Alessio
Brandon D'Alessio
214 Points

Confusion about Remainders

I understand that 7 % 3 = 1, but why does 3 % 7 = 3 & 5 % 7 = 5?

Thanks!

1 Answer

Walter Somerville
Walter Somerville
20,698 Points

With the % operator, the result is the number you get when subtracting the highest multiple of the number you are dividing by from the number that is being divided. 

// 6 is the max multiple of 3 (3(2))that is still below 7 (the next would be 9).  
3 * 2 = 6

// however it is still one less than seven, making the remainder 1. 
7-6 = 1

so for 3 % 7:

// Because 7 cannot go into 3 or 5 even once without producing something other than a whole number, 
// the multiple of 7 is 0
7 * 0 = 0 

//resulting in the remainder being the entire number that was being divided.
3 - 0 = 3

Hope that helps, I doubt thats how a mathematician would explain it, but it's how I've always thought about it.

Brandon D'Alessio
Brandon D'Alessio
214 Points

It does. Thanks!