Greatest Common Divisor (GCD) of 186 and 31
The greatest common divisor (GCD) of 186 and 31 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 186 and 31?
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 | 186 ÷ 31 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 140 and 137 | 1 |
| 179 and 169 | 1 |
| 125 and 101 | 1 |
| 185 and 103 | 1 |
| 72 and 97 | 1 |