Greatest Common Divisor (GCD) of 122 and 134
The greatest common divisor (GCD) of 122 and 134 is 2.
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 122 and 134?
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 | 122 ÷ 134 = 0 remainder 122 |
| 2 | 134 ÷ 122 = 1 remainder 12 |
| 3 | 122 ÷ 12 = 10 remainder 2 |
| 4 | 12 ÷ 2 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 184 and 97 | 1 |
| 138 and 82 | 2 |
| 126 and 197 | 1 |
| 117 and 174 | 3 |
| 161 and 101 | 1 |