A operator calculator computes the remainder when one number (the dividend) is divided by another (the divisor), represented as a mod b.
How It Works
Mathematical Definition: For two integers
a(dividend) andb(divisor),a mod bgives the remainder after dividingabyb.Formula:
a mod b = a - (b × floor(a/b)), wherefloor(a/b)is the largest integer less than or equal toa/b.Example:
16 mod 3 = 1because 16 ÷ 3 = 5 with a remainder of 1.15 mod 3 = 0because 15 is perfectly divisible by 3.
Online Tools
Several free online calculators perform modulo operations instantly:
BYJU’S Mod Calculator: Enter two numbers and get the result in seconds.
Cuemath Mod Calculator: Provides step-by-step solutions.
Calculator.io Modulo Calculator: Supports positive, negative, and decimal numbers.
EasyMathTools Modulo Calculator: Handles complex expressions and negative numbers.
Using Scientific Calculators
Many scientific calculators (e.g., Casio fx-991EX) lack a dedicated mod button. Workarounds:
Fraction Method: Enter
a/b, pressShift + S<=>Dto convert to a mixed fraction. The numerator of the fractional part is the remainder.Example:
153 ÷ 5 = 30 + 3/5 → 153 mod 5 = 3
Manual Method: Divide
abyb, take the integer part of the quotient, multiply it byb, then subtract froma.Example:
179 ÷ 17 ≈ 10.529,17 × 10 = 170,179 - 170 = 9 → 179 mod 17 = 9
Programming Languages
Most programming languages use % as the modulo operator:
Python:
17 % 5returns2JavaScript:
17 % 5returns2C++:
17 % 5returns2
⚠️ Note: Behavior with negative numbers varies by language. For example, in Python,
-5 % 3 = 1, while in some languages it may return-2.
For modular exponentiation (e.g., 5^15 mod 23), use specialized tools like dCode’s Modular Exponentiation Calculator or implement fast algorithms like binary exponentiation.
modular arithmetic - How to calculate a Modulo? - Mathematics Stack Exchange
Does anyone know how to do Modulo operations in this Calculator?
Can the Mac OS calculator do modulus?
TI-84 Plus modulo
What is a modulo calculator?
How can I use the modulo operator in Python?
How does a modulo calculator work internally?
Videos
When you see "modulo", especially if you are using a calculator, think of it as the remainder term when you do division.
Examples:
The result of 10 modulo 5 is 0 because the remainder of 10 / 5 is 0.
The result of 7 modulo 5 is 2 because the remainder of 7 / 5 is 2.
The reason your calculator says 113 modulo 120 = 113 is because 113 < 120, so it isn't doing any division.
More generally, the idea is that two numbers are congruent if they are the same modulo a given number (or modulus)
For example, as above, 
where 
is our modulus.
Another issue is that of inverses, which is where the confusion of 
comes in.
We say that 
and 
are inverses modulo 
, if 
, and we might write 
.
For example $17\cdot 113 = 1921 = 120\cdot 16 +1 \equiv 1 \mod 120
17^{-1} = 113$ modulo 
.
There are ways to calculate it, modulo is remainder counting basically.
because 
because 
and so on, so if you want to calculate for example 
you can do this, that is want to get 
, take 73 and continue subtracting 7 until you no longer can. 
, 
etc until we get 
which gives us that 
in it's simplest form (any of the results along the way can technically be a).
As for what 
the question is simply what times 17 gives remainder 1 when divided by 120?
$113\cdot 17 = 1921 = 120\cdot 16+1$