Greatest Common Divisor (GCD) of 155 and 186
The greatest common divisor (GCD) of 155 and 186 is 31.
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 155 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 | 155 ÷ 186 = 0 remainder 155 |
| 2 | 186 ÷ 155 = 1 remainder 31 |
| 3 | 155 ÷ 31 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 148 and 79 | 1 |
| 160 and 159 | 1 |
| 113 and 17 | 1 |
| 119 and 197 | 1 |
| 58 and 18 | 2 |