# Modulo calculator

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.

In practical terms, you can think of this process like making change. Need to pass an answer to a friend? It's easy to link and share the results of this calculator. 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. 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 divisora modulo n often written as as a mod n is the remainder of the Euclidean division of a by n.

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 is theoretically encryption but is a fairly weak form of encryptions by the standards of modern technology. Mod Calculator Online Math Tools.

Modulo Calculator Base. What does a modulo operation do? Practical Example: Modulo Calculator In practical terms, you can think of this process like making change. What is the modulo operation?

Can someone show me a general step-by-step procedure on how I would be able to find out the 5 modulo 10, or 10 modulo 5. Because when I calculate using a calculator modulothe result is When you see "modulo", especially if you are using a calculator, think of it as the remainder term when you do division.

More generally, the idea is that two numbers are congruent if they are the same modulo a given number or modulus. There are ways to calculate it, modulo is remainder counting basically.

Modulo is counting when knowing only a limited amount of numbers. As you can see, you will end up at zero whenever the actual number is divisible by three. So finding the nearest multiples of three will help you to find its value moldulo three. As explained in the other answers you could have found this using division with rest. A simple way to understand this "modulo" operation. We can travel on the other direction also. Sign up to join this community. The best answers are voted up and rise to the top.

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Email Required, but never shown. The Overflow Blog.In computingthe modulo operation should see Common pitfalls below find the remainder after division of one number by another called the modulus of the operation.

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Given two positive numbers, a and na modulo n abbreviated as a mod n is the remainder of the Euclidean division of a by nwhere a is the dividend and n is the divisor. For example, the expression "5 mod 2" would evaluate to 1 because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 because the division of 9 by 3 has a quotient of 3 and leaves a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3.

Doing the division with a calculator will not show the result referred to here by this operation; the quotient will be expressed as a decimal fraction. Although typically performed with a and n both being integers, many computing systems allow other types of numeric operands. See modular arithmetic for an older and related convention applied in number theory. When either a or n is negative, the naive definition breaks down, and programming languages differ in how these values are defined. In mathematicsthe result of the modulo operation is an equivalence classand any member of the class may be chosen as representative; however, the usual representative is the least positive residuethe smallest non-negative integer that belongs to that class, i.

However, other conventions are possible. Computers and calculators have various ways of storing and representing numbers; thus their definition of the modulo operation depends on the programming language or the underlying hardware.

In nearly all computing systems, the quotient q and the remainder r of a divided by n satisfy.

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However, this still leaves a sign ambiguity if the remainder is nonzero: two possible choices for the remainder occur, one negative and the other positive, and two possible choices for the quotient occur.

Usually, in number theory, the positive remainder is always chosen, but programming languages choose depending on the language and the signs of a or n.

See the table for details. Boute argues that Euclidean division is superior to the other ones in terms of regularity and useful mathematical properties, although floored division, promoted by Knuth, is also a good definition.

Despite its widespread use, truncated division is shown to be inferior to the other definitions. As neither floor division nor Euclidean division offer this symmetry, Boute's judgement is at least incomplete. When the result of a modulo operation has the sign of the dividend, it can lead to surprising mistakes. For example, to test if an integer is odd, one might be inclined to test if the remainder by 2 is equal to One correct alternative is to test that the remainder is not 0 because remainder 0 is the same regardless of the signs :.

Some calculators have a mod function button, and many programming languages have a similar function, expressed as mod anfor example. Modulo operations might be implemented such that a division with a remainder is calculated each time.

For special cases, on some hardware, faster alternatives exist.

## Modular arithmetic

For example, the modulo of powers of 2 can alternatively be expressed as a bitwise AND operation:. In devices and software that implement bitwise operations more efficiently than modulo, these alternative forms can result in faster calculations. This simple optimization is not possible for languages in which the result of the modulo operation has the sign of the dividend including Cunless the dividend is of an unsigned integer type.

Some modulo operations can be factored or expanded similarly to other mathematical operations. This may be useful in cryptography proofs, such as the Diffie—Hellman key exchange. In that case, d is called an offset. There does not seem to be a standard notation for this operation, so let us tentatively use a mod d n. The operation of modulo with offset is related to the floor function as follows:.Enter two numbers, with the first number a being the dividend while the second smaller number n is the divisor.

People use modular arithmetic all the time, especially with anything involving remainders, time and calendar schedules. Modular arithmetic, sometimes called clock arithmetic, is a calculation that involves a number that resets itself to zero each time a whole number greater than 1, which is the mod, is reached.

An example of this is the hour digital clock, which resets itself to 0 at midnight. The standard format for mod is: a mod n Where a is the value that is divided by n. Instead of its decimal form 0. One might presume the mod function generates the same values as positive numbers when one number is negative. This is actually not the case. For instance, if you have mod 60the remainder is But if you have mod 60the remainder is Why does this happen?

But withwe subtract a number with a greater absolute valueso the mod function generates a positive value. The resulting remainder is also smaller compared to when both numbers are positive. According to Britannicathe concept of modular arithmetic has been used by ancient civilizations such as the Indians and Chinese.

Moreover, modular arithmetic was used to solve astronomical and seasonal calculations which were problems associated with natural and man-made cycles. In Western mathematics, German mathematician and physicist Carl Friedrich Gauss did the first systematic study of modular arithmetic.

Gauss is regarded as one of the most influential figures in modern mathematics. In the number theory, scholars analyze the properties of natural numbers, which are whole numbers like -1, -2, 0, 1, 2, and so on. Their objective is to discover unexpected mathematical patterns and interactions between natural numbers. The residues are added by finding the arithmetic sum of the numbers, and the mod is subtracted from the sum as many times as possible. This diminishes the sum to a number M, which is between 0 and N — 1.

For instance, if we add the sum of 2, 4, 3 and 7, the sum is congruent to 6 mod This means 16 divided by 10 leaves a remainder of 6. This means 13 divided by 12 leaves a remainder of 1. Since we have 24 hours in a day, it makes sense to refer to time in a hour fashion.

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This is the principle behind the military time systembeginning at midnight with hours, and ending the hour at 11PM with hours. The military uses this to coordinate with bases and other personnel located in different time zones. Moreover, all pilots commercial or otherwise use the hour clock to avoid confusion while traveling between time zones. How is this connected with modulo?A modulo operation refers to the process of finding the remainder after dividing one number from another.

The modulo is also referred to as the modulus and you can use this modulo calculator to solve for it.

Inputting the values in the required fields allows the modular arithmetic calculator to perform the calculations accurately. To use this calculator, follow these steps:. An illustrative example can best show how to calculate modulo without using a modulo calculator. You need a mod 12 modulo operation.

There are other elaborate ways to use modulo operations in mathematics but the basic formula for modulo is:. A mod calculator is also known as a modular arithmetic calculator, a modular division calculator or a div calculator.

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But even without this online tool, you can solve for the modulo manually by following these steps:. Most of us are not even aware of its significance but this operation has many applications from math and science problems to everyday life. You can use modulo operations in the computation of checksums for serial numbers. Checksum refers to a digit representing the sum of digits in a piece of transmitted or stored digital data. As we have observed, check digits are mostly used for lengthy numbers and these are the digits calculated by algorithms.

You can use both the digits and the algorithm to alert you about any arising errors. You can also use modulo operations in:. On the lighter side, Modulo can be very useful in cases when you have to split or divide something.

One example in real-life is when you will share a pizza with your family. For instance, a pizza has 10 slices and there are three of you. How many slices would remain if you share it equally?

The answer is obvious but you can still represent this as a modulo operation:. Simply said, 10 divided by three is equal to 3 with a remainder of 1. You may think modulo is not necessary but when dealing with big figures, its usefulness becomes more apparent. Modulo Calculator Mod. Loading Calculator….

Correct Answer :. Let's Try Again :. Try to further simplify. Learning math takes practice, lots of practice. Just like running, it takes practice and dedication. If you want Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back Sign In Sign in with Office Sign in with Facebook.

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Please try again using a different payment method.When you work out a long division problem on your calculator, by default, it gives you the result as a whole number followed by a decimal with numbers after the decimal. But depending on the context for the division problem, you might require the answer as a whole number with a remainder instead. While most scientific calculators have a remainder function that you can locate either on the keyboard or by scrolling through their menus, this quick trick lets you calculate remainders with any calculator at all.

Work the division in your calculator as normal. Once you have the answer in decimal form, subtract the whole number, then multiply the decimal value that's left by the divisor of your original problem. The result is your remainder. For example, divide by 7 to arrive at Round this to a whole number of Subtract this from the original number of to arrive at a remainder of 3. Before you figure out a division problem with a calculator, it helps to have some basic terms straight.

The number divided into is the dividend, the number you're dividing it by is the divisor and the answer is the quotient. If you were to write your division problem out as a fraction, the number on top also called the numerator is the dividend, and the number on bottom also called the denominator is the divisor. Find the remainder of a division problem with your calculator, by working the division as usual.

## Modulo Calculator

You'll get a decimal answer — that's fine. Subtract the integer from the answer you received. That's whatever amount is to the left of the decimal point. You're left with only the part of the answer that was to the right of the decimal point. Multiply what's left of your answer by the initial divisor.

Multiply that by 8 and you have the remainder: 3. If you're writing out long division, the divisor is the number to the left outside of the long division sign. Lisa studied mathematics at the University of Alaska, Anchorage, and spent several years tutoring high school and university students through scary -- but fun! About the Author. Copyright Leaf Group Ltd.