Greatest Common Divisor (GCD) of 78 and 194
The greatest common divisor (GCD) of 78 and 194 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 78 and 194?
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 | 78 ÷ 194 = 0 remainder 78 |
| 2 | 194 ÷ 78 = 2 remainder 38 |
| 3 | 78 ÷ 38 = 2 remainder 2 |
| 4 | 38 ÷ 2 = 19 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 124 and 17 | 1 |
| 92 and 156 | 4 |
| 183 and 57 | 3 |
| 39 and 139 | 1 |
| 31 and 55 | 1 |