Greatest Common Divisor (GCD) of 102 and 185
The greatest common divisor (GCD) of 102 and 185 is 1.
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 185?
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 ÷ 185 = 0 remainder 102 |
| 2 | 185 ÷ 102 = 1 remainder 83 |
| 3 | 102 ÷ 83 = 1 remainder 19 |
| 4 | 83 ÷ 19 = 4 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 153 and 21 | 3 |
| 25 and 74 | 1 |
| 199 and 25 | 1 |
| 182 and 51 | 1 |
| 146 and 35 | 1 |