Modular Arithmetic

Modular arithmetic is a branch of Mathematics use to predict the outcomes of cyclic events such as days of the week, market days, months of the year, time etc.


  • The modulo value must be greater than the number worked upon.
  • When using cyclic pattern in adding numbers, you must count clock wise direction.
  • In subtraction of numbers , you must count anti -clock wise direction


The shorter hand of a clock points to 5 on a clock face.  What number does it point to after 30 hours?

modular arithmetic


30 hours after = 11 o” clock.

2. Find the following numbers in their simplest form in modulo 4

  1. 15 102


15(mod4) = 15÷4

3 remainder 3,   therefore 3 the remainder is taken as 3 mod 4

102mod4 = 102 ÷4   = 25 remainder 2

102 (mod 4) = 2 mod 4

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