Recognizing when to use the modulus operator

Question

I know the modulus (%) operator calculates the remainder of a division. How can I identify a situation where I would need to use the modulus operator?

I know I can use the modulus operator to see whether a number is even or odd and prime or composite, but that's about it. I don't often think in terms of remainders. I'm sure the modulus operator is useful, and I would like to learn to take advantage of it.

I just have problems identifying where the modulus operator is applicable. In various programming situations, it is difficult for me to see a problem and realize "Hey! The remainder of division would work here!".

Answer 1

Imagine that you have an elapsed time in seconds and you want to convert this to hours, minutes, and seconds:

h = s / 3600; m = (s / 60) % 60; s = s % 60; 

Answer 2

0 % 3 = 0; 1 % 3 = 1; 2 % 3 = 2; 3 % 3 = 0; 

Did you see what it did? At the last step it went back to zero. This could be used in situations like:

1. To check if N is divisible by M (for example, odd or even) or N is a multiple of M.

2. To put a cap of a particular value. In this case 3.

3. To get the last M digits of a number -> N % (10^M).