Greatest Common Divisor (GCD) of 513 and 190
The greatest common divisor (GCD) of 513 and 190 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 513 and 190?
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 | 513 ÷ 190 = 2 remainder 133 |
| 2 | 190 ÷ 133 = 1 remainder 57 |
| 3 | 133 ÷ 57 = 2 remainder 19 |
| 4 | 57 ÷ 19 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 55 and 79 | 1 |
| 121 and 168 | 1 |
| 152 and 113 | 1 |
| 187 and 118 | 1 |
| 49 and 108 | 1 |