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Modulo Calculator with Steps
Looking to execute modulo operations on numbers? Well, your search ends here! With this modulo calculator, you can find the results of mod operations with steps. All you have got to do is enter the initial number x and integer y in our calculator to determine the modulo number r.
What Exactly is Modulo?
Modulo, modular or simply, mod, is a mathematical operation that determines the remainder when one integer is divided by another.
For integers a and b:
$\mathbf{a mod b = r}$
Where
 ‘a’ stands for the dividend
 ‘b’ for divisor (or modulus)
 ‘r’ for the remainder
Modular Arithmetic Calculator
To try to give you intuitive insight into the modulo operation calculator without making stuff too complicated, we have illustrated the ‘clock’ example. Observe what happens when we increase numbers by one every time in this example.
The remainders begin from 0 and increase by 1 every time, until the point that the number reaches one less digit than the integer we are dividing by. When we reach this point, the sequence recycles.
With this illustration, we can picture the modulo operator in circles. We write 0 at the top of a circle and continue clockwise writing integers 1, 2, 3, 4 ... up to one less than our modulus: in this case, 12 i.e, a clock with the 12 replaced with 0 would be the circle for a modulus of 12.
To find the result of ‘a mod b’, check out the steps given below:
Work out this clock for size B
Begin at 0 and wind the clock ‘A’ steps
Wherever we land is our solution.
(If our number is positive, we step clockwise, if it's negative, we step anticlockwise.)
How to Calculate Modulo?
Calculating mod becomes relatively easier once you’ve known the formula and understood the concept of the modular arithmetic calculator with steps. All that’s left to do is find the remainder.
Mod Formula
For integers a and b:
$\Large{\mathrm{a mod b = r}}$
Let’s do some practical work now and show you how our mod calculator determines the results of modulo operations.
Below are some of the examples where we calculate modulo with the formula of the modulus operator calculator.
Modulo Calculation Example
Consider the following:
$\mathbf{Dividend} = a = 12$
$\mathbf{Divisor} = b = 5$
$\mathbf{Remainder} = r =?$
We work our way up by subtracting the dividend from the product of the quotient and the divisor.
a mod b $= a\Big(\Big\lbrack\dfrac{a}{b}\Big\rbrack\times b\Big)$
Putting values in mod formula
$12 \mathrm{mod} 5 = 12(\Big\lbrack\dfrac{12}{5}\Big\rbrack\times 5)$
When $12$ divided by $5$ gives us $2.4$, we round it down to the nearer number which in this case, is \(2\).
$12 \mathrm{mod} 5 = 12(2\times5)$
Now multiplying the quotient and the divisor,
$12 \mathrm{mod} 5 = 1210$
$\bold{12 \mathrm{mod} 5 = 52}$
Our modulo calculator can be used to determine the outcome between integer numbers of modulo operations.
The modulo operation, which is also frequently referred to as the modulus operation, identifies the remainder after dividing a given number by another number.
Apart from the abovementioned expression, it can also be expressed as ‘a percent b’ in specific cases. On conventional calculators, you can determine modulo b using mod () function: mod (a, b) = r.
Moreover, you can use our free online remainder calculator to get the remainder of the given values.
Modulus Operator Calculator
1: Cryptography
Modular arithmetic is one of the most significant aspects of cryptography, which codes information through modulo operations that have an exponentially large modulus.
It supports public key systems directly in cryptography such as RSA and Diffie–Hellman and offers finite fields that support elliptical curves. This modular math is used in a variety of key symmetric algorithms including the International Data Encryption Algorithm (IDEA), RC4, and Advanced Encryption Standard (AES). RSA and Diffie–Hellman uses modular exponentiation.
2: Programming
Are you a geek who is into programming? Well, you might find it interesting that taking the modulo is how you can adjust items in a hash table:
 Say your table has N entries.
 Alter the item key to a number.
 Do mod N, and put the item in that bucket while keeping a linked list there.
As your hash table increases in size, you can recompute the modulus for the keys.
3: Computational Applications
A modular arithmetic calculator is generally used in computer algebra to limit the size of integer coefficients in intermediate calculations and data.
It is also employed to factorize polynomials, a problem for which all known optimal algorithms use modular arithmetic.
On the other end, modular arithmetic has profound usability for bitwise operations and others involving cyclic fixedwidth data structures.
Fun Fact of Mod Calculator
Ever heard of the ‘NP’ set of computational problems? It stands for the Nondeterministic Polynomialtime. NP is part of the problem space (PSPACE) which contains problems related to computational complexity that are not solvable with deterministic
computers that take deterministic time for problemsolving. These are all the computers we know that can’t truly generate a random number due to the inherent determinism that governs our known laws of physics.
And it turns out that solving a system of nonlinear arithmetic equations is an NPcomplete problem, which means that they would take forever to solve in deterministic time with deterministic computers. This is part of the elegance of modular arithmetic.

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Best and only proper modulo calculator you can find on internet.