Modulo Calculator - Free Mod Calculator Online
Calculate modulus operations instantly. Find the remainder when dividing one number by another. Easy-to-use mod calculator with step-by-step explanation.
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A modulo calculator (also known as a mod calculator or modulus calculator) calculates the remainder when one number (the dividend) is divided by another number (the divisor). The modulo operation is denoted as "a mod b" or "a % b" and returns the remainder of the division.
How to Use the Modulo Calculator
- Enter Number (Dividend): Enter the number you want to divide (e.g., 29).
- Enter Divisor: Enter the number you want to divide by (e.g., 5).
- Click Calculate: Get the remainder (modulo result) instantly.
What is Modulo Operation?
The modulo operation (mod) finds the remainder after division. For example:
- 29 mod 5 = 4 because 29 ÷ 5 = 5 remainder 4
- 17 mod 3 = 2 because 17 ÷ 3 = 5 remainder 2
- 100 mod 7 = 2 because 100 ÷ 7 = 14 remainder 2
Modulo Formula
The modulo operation can be expressed as:
a mod b = remainder when a is divided by b
Or mathematically:
a mod b = a - (b × floor(a/b))
Where floor(a/b) is the integer division (quotient) of a by b.
Examples of Modulo Operations
- 10 mod 3 = 1 (10 ÷ 3 = 3 remainder 1)
- 20 mod 4 = 0 (20 ÷ 4 = 5 remainder 0, 20 is divisible by 4)
- 15 mod 7 = 1 (15 ÷ 7 = 2 remainder 1)
- 100 mod 25 = 0 (100 ÷ 25 = 4 remainder 0, 100 is divisible by 25)
- 27 mod 6 = 3 (27 ÷ 6 = 4 remainder 3)
Properties of Modulo Operation
- Range: The result of a mod b is always between 0 and (b-1) when b is positive.
- Zero Result: If a mod b = 0, then a is divisible by b.
- Identity: a mod 1 = 0 for all integers a.
- Negative Numbers: The behavior of modulo with negative numbers depends on the programming language or mathematical convention used.
Applications of Modulo
- Even/Odd Check: n mod 2 = 0 means even, n mod 2 = 1 means odd
- Cyclic Patterns: Used in clocks (12-hour format: hour mod 12), calendars, and circular arrays
- Hashing: Used in hash functions and hash tables in computer science
- Cryptography: Used in encryption algorithms like RSA
- Random Number Generation: Used to generate pseudo-random numbers
- Array Indexing: Used to wrap around array indices in circular buffers
Common Use Cases
- Check Divisibility: If a mod b = 0, then a is divisible by b
- Find Last Digit: Number mod 10 gives the last digit
- Day of Week Calculation: Used in calendar calculations
- Modular Arithmetic: Used in number theory and cryptography
Frequently Asked Questions
What is modulo operation?
The modulo operation (mod) finds the remainder after dividing one number by another. For example, 29 mod 5 = 4 because 29 divided by 5 equals 5 with a remainder of 4.
How do you calculate modulo?
To calculate a mod b, divide a by b and find the remainder. For example, 17 mod 3 = 2 because 17 ÷ 3 = 5 remainder 2. The modulo result is always between 0 and (b-1) when b is positive.
What does it mean when modulo is 0?
When a mod b = 0, it means that a is divisible by b with no remainder. For example, 20 mod 4 = 0 means 20 is divisible by 4.
What is the difference between modulo and division?
Division gives you the quotient (how many times one number fits into another), while modulo gives you the remainder (what's left after division). For example, 29 ÷ 5 = 5.8 (quotient), while 29 mod 5 = 4 (remainder).
How is modulo used in programming?
Modulo is commonly used in programming for checking even/odd numbers (n mod 2), array indexing with wraparound, hash functions, generating random numbers, and implementing cyclic patterns or clocks.
Can modulo be negative?
The behavior of modulo with negative numbers depends on the implementation. In most programming languages and mathematical conventions, the result is always non-negative when the divisor is positive. For example, -5 mod 3 = 1 (not -2).