Greatest Common Divisor (GCD) of 139 and 92
The greatest common divisor (GCD) of 139 and 92 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 139 and 92?
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 | 139 ÷ 92 = 1 remainder 47 |
| 2 | 92 ÷ 47 = 1 remainder 45 |
| 3 | 47 ÷ 45 = 1 remainder 2 |
| 4 | 45 ÷ 2 = 22 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 107 and 34 | 1 |
| 47 and 141 | 47 |
| 149 and 108 | 1 |
| 100 and 134 | 2 |
| 138 and 65 | 1 |