Greatest Common Divisor (GCD) of 195 and 119
The greatest common divisor (GCD) of 195 and 119 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 195 and 119?
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 | 195 ÷ 119 = 1 remainder 76 |
| 2 | 119 ÷ 76 = 1 remainder 43 |
| 3 | 76 ÷ 43 = 1 remainder 33 |
| 4 | 43 ÷ 33 = 1 remainder 10 |
| 5 | 33 ÷ 10 = 3 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 129 and 156 | 3 |
| 144 and 48 | 48 |
| 15 and 20 | 5 |
| 84 and 20 | 4 |
| 181 and 25 | 1 |