R Modulo Remainder. Still, this is kind of querky in a mathematical sense because integer part product (kq) actually exceeds the dividend (x), thus defining the remainder (r) as a negative integer. Which is the remainder of a modulo operation?

Consider the positive modulo 19 mod 12using a clock:

That’s where we get into the weird gray area: For example, the expression 5 mod 2 would evaluate to 1, because 5 divided by 2 has a quotient of 2 and Mod (n, m) is the modulo operator and returns n mod m. The answer to this problem is understanding the difference between a remainder and a modulo.