Greatest Common Divisor (GCD) of 139 and 198
The greatest common divisor (GCD) of 139 and 198 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 198?
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 ÷ 198 = 0 remainder 139 |
| 2 | 198 ÷ 139 = 1 remainder 59 |
| 3 | 139 ÷ 59 = 2 remainder 21 |
| 4 | 59 ÷ 21 = 2 remainder 17 |
| 5 | 21 ÷ 17 = 1 remainder 4 |
| 6 | 17 ÷ 4 = 4 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 133 and 185 | 1 |
| 196 and 137 | 1 |
| 135 and 69 | 3 |
| 86 and 35 | 1 |
| 121 and 44 | 11 |