Greatest Common Divisor (GCD) of 34 and 102
The greatest common divisor (GCD) of 34 and 102 is 34.
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 34 and 102?
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 | 34 ÷ 102 = 0 remainder 34 |
| 2 | 102 ÷ 34 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 180 and 30 | 30 |
| 95 and 158 | 1 |
| 144 and 35 | 1 |
| 22 and 124 | 2 |
| 38 and 142 | 2 |