Greatest Common Divisor (GCD) of 130 and 180
The greatest common divisor (GCD) of 130 and 180 is 10.
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 180?
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 ÷ 180 = 0 remainder 130 |
| 2 | 180 ÷ 130 = 1 remainder 50 |
| 3 | 130 ÷ 50 = 2 remainder 30 |
| 4 | 50 ÷ 30 = 1 remainder 20 |
| 5 | 30 ÷ 20 = 1 remainder 10 |
| 6 | 20 ÷ 10 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 180 and 19 | 1 |
| 188 and 141 | 47 |
| 157 and 126 | 1 |
| 21 and 21 | 21 |
| 177 and 135 | 3 |