Greatest Common Divisor (GCD) of 138 and 185
The greatest common divisor (GCD) of 138 and 185 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 138 and 185?
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 | 138 ÷ 185 = 0 remainder 138 |
| 2 | 185 ÷ 138 = 1 remainder 47 |
| 3 | 138 ÷ 47 = 2 remainder 44 |
| 4 | 47 ÷ 44 = 1 remainder 3 |
| 5 | 44 ÷ 3 = 14 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 157 and 189 | 1 |
| 107 and 156 | 1 |
| 121 and 10 | 1 |
| 40 and 186 | 2 |
| 109 and 131 | 1 |