Greatest Common Divisor (GCD) of 130 and 198
The greatest common divisor (GCD) of 130 and 198 is 2.
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 130 and 198?
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 | 130 ÷ 198 = 0 remainder 130 |
| 2 | 198 ÷ 130 = 1 remainder 68 |
| 3 | 130 ÷ 68 = 1 remainder 62 |
| 4 | 68 ÷ 62 = 1 remainder 6 |
| 5 | 62 ÷ 6 = 10 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 157 and 122 | 1 |
| 162 and 171 | 9 |
| 136 and 102 | 34 |
| 145 and 190 | 5 |
| 78 and 62 | 2 |