Greatest Common Divisor (GCD) of 190 and 189
The greatest common divisor (GCD) of 190 and 189 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 190 and 189?
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 | 190 ÷ 189 = 1 remainder 1 |
| 2 | 189 ÷ 1 = 189 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 194 and 63 | 1 |
| 120 and 21 | 3 |
| 60 and 38 | 2 |
| 51 and 131 | 1 |
| 186 and 166 | 2 |