I can write the program
int a = 3;
int b = 4;
Console.WriteLine(a % b);
The answer I get is 3. How does 3 mod 4 = 3???
I can't figure out how this is getting computed this way.
7 Answers
I found the accepted answer confusing and misleading.
Modulus is NOT the same as modern division that returns a ratio of dividend and divisor. This is often expressed as a decimal quotient that includes the remainder in the quotient. That is what trips people up.
Modulus is just the remainder in division before its used in a decimal quotient.
Example: The division of two numbers is often expressed as a decimal number (quotient). But the result of the division of say, 1/3, can also be expressed in whole numbers as "0 with a remainder of 1". But that form of quotient is not very helpful in modern math, so a decimal value or the ratio of the two numbers is often what we see returned in modern calculators.
1 / 3 = .333333333......
But modulus does not work that way. It ignores the decimal quotient value or ratio returned from division, takes the quotient expression of "0 with a remainder of 1" in 1/3, and extracts the 1 or remainder that was returned from that division. It just strips out the remainder from the quotient and spits back the remainder of division before its converted to a decimal. Below is how modulus works...
1 % 3 = 1
As such, a better way of describing Modulus is to say it is what is left over as an integer (remainder) in the first number (dividend) after dividing the second number (divisor) into it as many times as possible.
1 % 1 = 0 because after dividing 1 into 1, one time, there's nothing left
2 % 1 = 0 because after dividing 1 into 2, two times, there's nothing left
1 % 2 = 1 because 2 won't go into 1, so 1 is left
These whole number remainders returned by modulus (modular math) are useful in software programs in extracting the day of a week, creating alternating sequences, finding if a number is even or odd, etc.
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