A method for finding remainders where all the possible numbers (the numbers less than the divisor) are put in a circle, and then by counting around the circle the number of times of the number being divided, the remainder will be the final number landed on.

An arithmetic system based on the remainder obtained when dividing a given number by the base number which is called a modulus.

two numbers are considered equal (congruent) if heir difference is divisible by the base. Thus, . Numbers are represented by integers between and , where is the base. Multiplication, addition, and subtraction are normal, except that the results are reduced. Division is performed by reducing fractions to least terms, applying an extended Euclid's algorithm to find the inverse of the denominator, and then performing multiplication. Symbol: mod

a form of arithmetic where integers are considered equal if they leave the same remainder when divided by the modulus.

Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value — the modulus. Modular arithmetic was introduced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.