Modulo Calculator

Quotient: 14, remainder:2.

Tool Overview: Mod Calculator

What does a modulo operation do?

This modulo calculator is used to perform modular arithmetic. The mod calculator takes two numbers and divides the second into the first. It returns a quotient and a remainder. The quotient is the greatest whole number of times the second number can be divided into the first without the remainder becoming negative. The remainder is the amount left over after the division operation. Mathematically, this process is referred to as the modulo operation. This could also be called a quotient and remainder calculator.

Modulo definition: What is the modulo operator?

The modulo operator (aka the modulus operator), written as %, generates the remainder of the integer division of two integer numbers. This is implemented as the mod function in programming.

This website is a modular arithmetic calculator (modulus calculator). The input number undergoes a modulo calculation for the remainder operator.

What does congruent modulo n mean?

Two integers are congruent modulo if they have the same remainder for a given divisor n.

Practical Example: Modulo Calculator

In practical terms, you can think of this process like making change. If I went a garage sale with a twenty dollar bill and discovered a box of 8-track music tapes priced at $3 each, how many tapes could I buy and how much would be left over? In this case, I would enter a 20 in the first box of the online mod calculator (the base) and the price of the record ($3) into the second box of the mod calculator. This modulo calculator would then return a result: I can buy 6 records (the quotient) and would have $2 left over (the remainder).

Sharing Results of The Mod Calculator

Need to pass an answer to a friend? It's easy to link and share the results of this calculator. Simply use the following format: Number)&divi=(Your Other Number)

FAQ - More About The Mod Calculator

How do you calculate mod?

The modulo calculator uses various computer libraries to execute this efficiently. The pen and paper solution is to repeatedly subtract the divisor from the base number until the remainder is less than the divisor. In many cases, this process is accelerated with lookup tables. The modulo calculation is of keen interest to researchers due to its role in many important computing processes.

What is the modulo operation?

Here is how to how to calculate modulus. The modulo operation finds the remainder after division of one number by another . For two positive numbers, a (the dividend) and n (the divisor), a modulo n (often written as as a mod n) is the remainder of the Euclidean division of a by n.

What is mod26?

An algebraic implementation of the modulo operation where you can map numbers into the alphabet. You take a number, convert it into base 26 math and map the values into letters. This allows you to compress / encode the message as a text string. This is theoretically encryption but is a fairly weak form of encryptions by the standards of modern technology.

How does this relate to the check digit algorithm?

Many check digit systems use modular arithmetic to look for transmission errors in long series of numbers. The odds of getting the remainder value correct by random chance are very low.

What is modular exponentiation?

Modular exponentiation is a rapid way of calculating the remainder of an integer raised to a power and divided by another integer. Due to certain shortcuts (the Euclidean algorithm), this mathematical operation can be done quickly while the inverse operation ( computing a modular discrete logarithm) is an extremely slow operation. This is known as a one way problem (easy to solve one way, hard to solve in reverse) which makes it useful for activities such as public key cryptography.

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