How does modulus work exactly? [duplicate]

This question already has answers here: How Does Modulus Divison Work (19 answers) Closed 9 years ago.

I know what modulus (%) does, it gives you the remainder. But how does it do that? I saw that it uses the formula: modulus = dividend - (dividend / divisor) * divisor 10%3 should give you 1 (10 being the dividend and 3 being the divisor) the forumla gives: 10-(10/3)*3 = 10-10 = 0 which is obviously wrong.

Then again, working with pure variables, dividend - ( dividend / divisor ) * divisor = dividend - dividend = 0

What am I doing wrong here? (Also, the form开发者_开发知识库ula is from a native from JASS, the language used in warcraft 3 games)

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in the formula (dividend / divisor) is an integer division evaluating to an integer.

So, 10-(10/3)*3 = 10 - 9 = 1

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In many programming languages using C, C++, Java, etc. 10/3 would result in 3 because divisions are actually integer-divisions and the fractional part is truncated.

So, in other words n/d gives you only the quotient.

Now, from arithmetic we know that any positive integer n and any positive integer divider d, n can be represented as: n = q*d + r. If 0 ≤ r < n (and it can be proven that there is only one such positive r that is less than n), q is called the quotient and r is the called the remainder.

In these programming languages, n/d gives you q.

So, n - (n/d)*d = n - q*d = r, the remainder.