Greatest Common Divisor (GCD) of 95 and 38
The greatest common divisor (GCD) of 95 and 38 is 19.
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 95 and 38?
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 | 95 ÷ 38 = 2 remainder 19 |
| 2 | 38 ÷ 19 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 51 and 80 | 1 |
| 164 and 129 | 1 |
| 186 and 187 | 1 |
| 184 and 115 | 23 |
| 95 and 94 | 1 |