Greatest Common Divisor (GCD) of 126 and 125
The greatest common divisor (GCD) of 126 and 125 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 126 and 125?
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 | 126 ÷ 125 = 1 remainder 1 |
| 2 | 125 ÷ 1 = 125 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 114 and 110 | 2 |
| 120 and 167 | 1 |
| 103 and 182 | 1 |
| 136 and 124 | 4 |
| 157 and 197 | 1 |