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 u

Answer 1

Converting linear data structure to matrix structure: where a is index of linear data, and b is number of items per row:

row = a/b
column = a mod b

Note above is simplified logic: a must be offset -1 before dividing & the result must be normalized +1.

Example: (3 rows of 4)

1  2  3  4    
5  6  7  8    
9 10 11 12 

(7 - 1)/4 + 1 = 2

7 is in row 2

(7 - 1) mod 4 + 1 = 3 

7 is in column 3

Another common use of modulus: hashing a number by place. Suppose you wanted to store year & month in a six digit number 195810. month = 195810 mod 100 all digits 3rd from right are divisible by 100 so the remainder is the 2 rightmost digits in this case the month is 10. To extract the year 195810 / 100 yields 1958.