Greatest Common Divisor (GCD) of 102 and 38
The greatest common divisor (GCD) of 102 and 38 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 102 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 | 102 ÷ 38 = 2 remainder 26 |
| 2 | 38 ÷ 26 = 1 remainder 12 |
| 3 | 26 ÷ 12 = 2 remainder 2 |
| 4 | 12 ÷ 2 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 175 and 64 | 1 |
| 65 and 111 | 1 |
| 138 and 104 | 2 |
| 28 and 120 | 4 |
| 197 and 180 | 1 |