Greatest Common Divisor (GCD) of 82 and 131
The greatest common divisor (GCD) of 82 and 131 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 131?
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 ÷ 131 = 0 remainder 82 |
| 2 | 131 ÷ 82 = 1 remainder 49 |
| 3 | 82 ÷ 49 = 1 remainder 33 |
| 4 | 49 ÷ 33 = 1 remainder 16 |
| 5 | 33 ÷ 16 = 2 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 105 and 188 | 1 |
| 188 and 106 | 2 |
| 69 and 138 | 69 |
| 185 and 18 | 1 |
| 171 and 97 | 1 |