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Modulo Calculator

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Last updated date: 13th Jul 2024
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What is a Modulo?

Modulo is a vital part of mathematics. The residue following dividing one integer by another is known as the modulo (also known as "modulus" or perhaps even "mod"). For example, 1000 mod 9 is 1 as 1000/9 is 111, with a remainder of 1, which may be calculated using a modular division calculator. It's a term that's typically used to say that two different mathematical entities can be considered equivalent if their differences are compensated for by a third element. 

It is quite a simple topic to learn and it all revolves around the basics of remainders; something you’re unknowingly using every single day, even without using any modular arithmetic calculator. For example, when calculating hours, we tend to count up to twelve and then begin over at one. As a result, it is 1 p.m. 4 hours past 9 pm. Congruent modulo 12 refers to integers that vary by a factor of the modulus 12. In the same way, the days of the week, that are calculated modulo seven, are in a similar predicament. How to calculate modulus? Well, let's say it's Thursday. Which day will it be 1,000 days from now? We do not have to tally through all the 1,000 days; simply divide 1,000/7 to get the remaining, which would be 6. Then, a thousand days from now, the day should be the same as it was six days ago, a Wednesday. All of this can be calculated by using any modulo operator calculator.  

What is a Modulo Calculator?

Any modular calculator with steps allows the user to enter two values, with the very first value 'a' representing the dividend and the other number 'n' representing the divisor. After that, this application will do modulo operations to determine how many times this second number is solvable by the first integer, as well as determine the remainder on dividing.

So how to find mod? Whenever users click out of any form field, computations are done instantaneously; as it runs on certain algorithms that allow the calculator tool to run using the same predetermined procedure that lets the tool decide the final solution.

How to Calculate Modulo in a Calculator?

This is a very easy and simple step that you can follow if you want to know how to calculate modulus. For example, say you are given 2 numbers which are 7 and 3. The steps to calculate 7MOD3 is:

  1. Divide the two numbers. That would be 7/3 = 2.333333. 

  2. The next step is to remove the decimal part. This would make 2.333333 into 2. 

Something to always keep in your mind is that after you divide two numbers, if the answer does not contain any decimal part, then the modulus value would be 0. For example, if the 2 numbers you have are 8 and 4 and if you do 8/4 you get 2, so because there is nothing after the decimal part, the modulo calculator with steps would show 6MOD2=0

  1. After that step, the next step is to multiply the divisor with the number you got. That would be 2 x 3 = 6

  2. After that subtract the result from the dividend. 7 - 6 = 1. This is your mod value. Therefore 7MOD3 = 1. 

Now, this was a long process without the calculator. With a modulo operator calculator, it is just 2 easy steps. 

For example, you are given the question 33MOD4. How to find mod? With a scientific calculator, you have to do only 2 steps. 

  1. First, divide the two numbers. 33/4 would be 8.25. Then eliminate the decimals which would leave you with 8 from 8.25 after eliminating. 

  2. Then do 33 - (8x4) in your calculator which would give you your answer in a fraction of a second. The answer would be 1. So, the answer to your question is 33MOD4 = 1. 

This is the best and most efficient way of calculating mod in calculator.

Solved Example 

Find the interval of x for |x² – 5x + 6| and solve the modulus. How would you solve this without using a modular division calculator?

Solution: |x²– 5x + 6| = | (x – 2) (x – 3) | = |f(x)|

According to the modulus definition, 

|f(x)| = f(x); if f(x) is positive

| f(x) |= -f(x); if f(x) is negative

f(x) = (x – 2) (x – 3) is positive or zero when x = (- ∞, 2] ∪ [3, ∞)

f(x) = (x – 2) (x – 3) is negative when x = (2, 3)

So, |x²– 5x + 6| = (x²– 5x + 6) when x = (-∞, 2] ∪ [3, ∞) and |x²– 5x + 6| = -(x² – 5x + 6) when x = (2, 3)

You can also get help from a modulo calculator with steps to show you how to calculate. 

FAQs on Modulo Calculator

1) How to find the mod of a negative number?

Whenever one integer is negative, one could assume that the modulus function produces the very same results as positive numbers. This isn't the reality whatsoever. Use any mod function calculator to confirm.


When you have 340 modulo 60, for example, the leftover is 40.

However, the remainder will be 20 in case you have -340 mod 60! See? Completely different.


So, why would this happen in the first place? Because the multiple removed from a positive integer like 340 will be less than the absolute amount, hence the outcome becomes 40, just as proved using any modular division calculator.


-340, on the other hand, subtracts an integer with a higher upper bound, resulting in a positive value for the modulus operator. If both integers are positive, the resultant remainder too is lower.


So, we can say, for a negative number, the formula could be represented as: a mod n = a – r * n.

2) When and why should we use a modular arithmetic calculator?

There are multiple such occasions when you may opt to use a mod function calculator, and when you want to save up some time or can’t just understand what you’re doing, it’s better to let the tool do it for you.


For instance, you may use the modular division calculator for the conversions of units for measuring. Converting units of measure is a common example of the modulo operation’s practical utility. The general use case is when you want to convert a smaller unit, such as minutes or inches/centimeters, to a larger unit, like hours or miles/kilometers; in these situations, decimals or fractions aren’t always helpful. Apart from knowing when and why to use it, it is also important to know how to calculate mod in the calculator. 


For example, if we wanted to know the number of hours in 349 minutes, having the result expressed as 5 hours 49 minutes may be more helpful than 5.8167 hours. You can also use this to learn how to calculate mod in calculator.