Greatest Common Divisor (GCD) of 190 and 133
The greatest common divisor (GCD) of 190 and 133 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 190 and 133?
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 ÷ 133 = 1 remainder 57 |
| 2 | 133 ÷ 57 = 2 remainder 19 |
| 3 | 57 ÷ 19 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 118 and 106 | 2 |
| 119 and 84 | 7 |
| 126 and 112 | 14 |
| 169 and 72 | 1 |
| 189 and 174 | 3 |