
Greatest Common Divisor (GCD) of 82 and 113
The greatest common divisor (GCD) of 82 and 113 is 1.
What is the Greatest Common Divisor (GCD)?
The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It is useful in simplifying fractions, finding common factors, and in number theory.
How to Calculate the GCD of 82 and 113?
We use the Euclidean algorithm, which involves the following steps:
- Divide the larger number by the smaller number.
- Replace the larger number with the smaller number and the smaller number with the remainder from the division.
- Repeat this process until the remainder is zero.
- The non-zero remainder just before zero is the GCD.
Step-by-Step Euclidean Algorithm
Step | Calculation |
---|---|
1 | 82 ÷ 113 = 0 remainder 82 |
2 | 113 ÷ 82 = 1 remainder 31 |
3 | 82 ÷ 31 = 2 remainder 20 |
4 | 31 ÷ 20 = 1 remainder 11 |
5 | 20 ÷ 11 = 1 remainder 9 |
6 | 11 ÷ 9 = 1 remainder 2 |
7 | 9 ÷ 2 = 4 remainder 1 |
8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
193 and 182 | 1 |
197 and 36 | 1 |
103 and 115 | 1 |
104 and 76 | 4 |
198 and 99 | 99 |