x mod y = r

Modulo Calculator

The modulo calculator finds the solution of an expression x mod y = r.

This modulo calculator is a handy tool for finding the result of modulo operations. All you have to do is input the initial number x and the integer y to find the modulo number r according to the equivalence x mod y = r. Read on to discover what exactly are the modulo operations and how to use this calculator correctly.

What are modulo operations?

Imagine a clock hanging on the wall. Let's say it is late at night - 11 pm. You wonder what will be the time when you wake up after 8 hours of sleep. You can't just add 8 to 11, as there is no such time as 19 am. What you do is perform a modulo operation (mod 12) - you add these two numbers and keep subtracting 12 until you get a number lower than 12 - in this case, 7. You just calculated you will wake up at 7 am.

Modulo operations in the case of the clock are so intuitive we don't even notice them. In mathematics, there are many types of more elaborate modulo operations that require more thought. We can write down that

x mod y = r is true if there exists such an integer q that y*q + r = x.

Otherwise speaking, the number r is the remainder of division, where x is the dividend and y is the divisor.

How to use our mod calculator?

It is extremely simple. Just follow the steps below!

  1. Start with choosing the initial number (before performing the modulo operation). Let's say it is 250.
  2. Choose the divisor. Let's choose it as 24; we will be hence calculating the value of 250 mod 24.
  3. Divide one number by the other, rounding down: 250 / 24 = 10. This is the quotient.
  4. Multiply the divisor by the quotient. Subtract this number from your initial number. 250 - 10 * 24 = 250 - 240 = 10.
  5. The number you obtained is the result of your operation. We can write it down as 250 mod 24 = 10.

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Modulo Calculator
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