Greatest Common Divisor (GCD) of 134 and 186
The greatest common divisor (GCD) of 134 and 186 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 134 and 186?
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 | 134 ÷ 186 = 0 remainder 134 |
| 2 | 186 ÷ 134 = 1 remainder 52 |
| 3 | 134 ÷ 52 = 2 remainder 30 |
| 4 | 52 ÷ 30 = 1 remainder 22 |
| 5 | 30 ÷ 22 = 1 remainder 8 |
| 6 | 22 ÷ 8 = 2 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 110 and 154 | 22 |
| 123 and 44 | 1 |
| 91 and 156 | 13 |
| 129 and 192 | 3 |
| 133 and 70 | 7 |