Greatest Common Divisor (GCD) of 194 and 118
The greatest common divisor (GCD) of 194 and 118 is 2.
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 118?
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 ÷ 118 = 1 remainder 76 |
| 2 | 118 ÷ 76 = 1 remainder 42 |
| 3 | 76 ÷ 42 = 1 remainder 34 |
| 4 | 42 ÷ 34 = 1 remainder 8 |
| 5 | 34 ÷ 8 = 4 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 18 and 65 | 1 |
| 187 and 125 | 1 |
| 130 and 192 | 2 |
| 189 and 117 | 9 |
| 88 and 153 | 1 |