Greatest Common Divisor (GCD) of 185 and 111
The greatest common divisor (GCD) of 185 and 111 is 37.
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 111?
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 ÷ 111 = 1 remainder 74 |
| 2 | 111 ÷ 74 = 1 remainder 37 |
| 3 | 74 ÷ 37 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 38 and 48 | 2 |
| 177 and 13 | 1 |
| 195 and 16 | 1 |
| 110 and 71 | 1 |
| 172 and 88 | 4 |