Modulo Calculator

Introduction to Modulo Operation

The modulo operation, symbolized as "mod", finds the remainder of division between two numbers. For instance, "5 mod 3" evaluates to 2, as 5 divided by 3 leaves a remainder of 2.

Understanding the Modulo Calculator

This tool simplifies finding the remainder of a division operation. Enter the dividend and divisor to calculate the modulo.

Formula and Calculation

The modulo operation is defined by the formula:

\[ a \mod n = r \]

where \( a \) is the dividend, \( n \) is the divisor, and \( r \) is the remainder.

Practical Applications

Modulo operations are crucial in computer science, mathematics, and various everyday scenarios.

Step-by-Step Guide to Using the Calculator

1. Input the Dividend: Enter the number you wish to divide.
2. Input the Divisor: Enter the number you wish to divide by.
3. Calculate: Press the calculate button to obtain the remainder.

Modulo Calculator - Frequently Asked Questions

1. How do you calculate modulo?

The modulo operation, denoted as \( a \mod n \), calculates the remainder when \( a \) is divided by \( n \).

2. What's 10 mod 3?

\( 10 \mod 3 = 1 \), because 10 divided by 3 leaves a remainder of 1.

3. How to solve 4 mod 2?

\( 4 \mod 2 = 0 \), because 4 is exactly divisible by 2.

4. How to calculate 3 mod 7?

\( 3 \mod 7 = 3 \), because 3 divided by 7 leaves a remainder of 3 since 3 is less than 7.

5. How to solve 7 mod 5?

\( 7 \mod 5 = 2 \), because 7 divided by 5 leaves a remainder of 2.

6. What is 5 in mod 5?

\( 5 \mod 5 = 0 \), because 5 is exactly divisible by 5.

7. Why 3 mod 5 is 3?

\( 3 \mod 5 = 3 \) because 3 divided by 5 is less than 1, leaving 3 as the remainder.

8. Why is 2 mod 4?

\( 2 \mod 4 = 2 \), because 2 divided by 4 is less than 1, leaving 2 as the remainder.

9. How to solve 8 mod 4?

\( 8 \mod 4 = 0 \), because 8 is exactly divisible by 4.

10. Why 5 mod 2 is 1?

\( 5 \mod 2 = 1 \), because 5 divided by 2 leaves a remainder of 1.

11. Why is 2 mod 5 equal to 2?

\( 2 \mod 5 = 2 \) because 2 divided by 5 is less than 1, leaving 2 as the remainder.

12. Why is 2 mod 3 equal to 2?

\( 2 \mod 3 = 2 \) because 2 divided by 3 is less than 1, leaving 2 as the remainder.

13. Is 37 congruent to 3 mod 7?

Yes, \( 37 \equiv 3 \mod 7 \) because both 37 and 3 give a remainder of 3 when divided by 7.

14. How do you solve 8 modulus 3?

\( 8 \mod 3 = 2 \), because 8 divided by 3 leaves a remainder of 2.

15. What is the inverse of 3 modulus 7?

The modular inverse of 3 modulo 7 is 5, because \( 3 \times 5 \equiv 1 \mod 7 \).