ABSTRACT
The greatest common divisor depends only on a congruence, which allows talking about congruence classes being relatively primarily to the modulus. The Division Algorithm tells that an even number is a number that leaves a remainder of 0 when divided by 2 and an odd number leaves a remainder of 1 when divided by 2. Although nobody would say that 14 and 96 are the same number, they do share the property of having the same remainder when divided by 2. The Chinese Remainder Theorem gives a new way of looking at congruences for composite moduli. If factor the modulus m into distinct prime powers, then either can look at a congruence mod m, or can look at a system of congruence mod these prime powers. Sometimes the latter are easier to work with. Many computer programs interpret 7 as equal to 3.
