Greatest Common Divisor (GCD) of 123 and 131
The greatest common divisor (GCD) of 123 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 123 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 | 123 ÷ 131 = 0 remainder 123 |
| 2 | 131 ÷ 123 = 1 remainder 8 |
| 3 | 123 ÷ 8 = 15 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 188 and 51 | 1 |
| 41 and 186 | 1 |
| 164 and 111 | 1 |
| 135 and 126 | 9 |
| 149 and 110 | 1 |