Greatest Common Divisor (GCD) of 185 and 114
The greatest common divisor (GCD) of 185 and 114 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 185 and 114?
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 | 185 ÷ 114 = 1 remainder 71 |
| 2 | 114 ÷ 71 = 1 remainder 43 |
| 3 | 71 ÷ 43 = 1 remainder 28 |
| 4 | 43 ÷ 28 = 1 remainder 15 |
| 5 | 28 ÷ 15 = 1 remainder 13 |
| 6 | 15 ÷ 13 = 1 remainder 2 |
| 7 | 13 ÷ 2 = 6 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 124 and 141 | 1 |
| 156 and 136 | 4 |
| 58 and 79 | 1 |
| 87 and 189 | 3 |
| 169 and 65 | 13 |