Greatest Common Divisor (GCD) of 194 and 127
The greatest common divisor (GCD) of 194 and 127 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 194 and 127?
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 | 194 ÷ 127 = 1 remainder 67 |
| 2 | 127 ÷ 67 = 1 remainder 60 |
| 3 | 67 ÷ 60 = 1 remainder 7 |
| 4 | 60 ÷ 7 = 8 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 173 and 97 | 1 |
| 161 and 35 | 7 |
| 200 and 136 | 8 |
| 196 and 56 | 28 |
| 81 and 103 | 1 |