# Dividing Large Numbers and Finding the Remainder

May 19th, 2015
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The "mod" operator in computer languages is simply the remainder. For example, 17 mod 3 = 2 ; because 17 / 3 = 5 rem 2 which in turn means 17 = 3 * 5 + 2

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Dividing Large Numbers and Finding the RemainderSome IIM Questions also been inserted giving deep insight into different number theory problemsModular ArithmeticThe "mod" operator in computer languages is simply the remainder. For example, 17 mod 3 = 2 ; because 17 / 3 = 5 rem 2 which in turn means 17 = 3 * 5 + 2Note:The Set of all Integers can be divided into 3 classes:There are some tricky issues when negative numbers are used, but that shouldn't ordinarily be necessary.In math (number theory), the term is used a little differently. The "modulus" is actually not the remainder, but the number you are dividing by; and "mod" is not an operator, but a label telling "in what sense two quantities are considered congruent, or equal." For example, we would say 17 = 11 (mod 3)(read as "17 is congruent to 11, modulo 3"), meaning that 17 and 11 both leave the SAME remainder when divided by 3. You probably won't see this usage if you are only reading about programming, but it's worth being aware of if you look deeper into the math behind it.The notation (mod 100) is common in a branch of mathematics called number theory. It refers to so-called "modular arithmetic."When it is taught in school, it is often called "clock arithmetic."The idea is the same as the one found in "casting out nines," except you will be "casting out hundreds." The idea is that if you do addition, subtraction, or multiplication, you can discard multiples of 100 either before or after th

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