Greatest Common Divisor (GCD) of 184 and 115
The greatest common divisor (GCD) of 184 and 115 is 23.
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 184 and 115?
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 | 184 ÷ 115 = 1 remainder 69 |
| 2 | 115 ÷ 69 = 1 remainder 46 |
| 3 | 69 ÷ 46 = 1 remainder 23 |
| 4 | 46 ÷ 23 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 198 and 30 | 6 |
| 166 and 66 | 2 |
| 48 and 165 | 3 |
| 115 and 166 | 1 |
| 158 and 42 | 2 |