Greatest Common Divisor (GCD) of 83 and 130
The greatest common divisor (GCD) of 83 and 130 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 83 and 130?
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 | 83 ÷ 130 = 0 remainder 83 |
| 2 | 130 ÷ 83 = 1 remainder 47 |
| 3 | 83 ÷ 47 = 1 remainder 36 |
| 4 | 47 ÷ 36 = 1 remainder 11 |
| 5 | 36 ÷ 11 = 3 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 191 and 166 | 1 |
| 50 and 55 | 5 |
| 46 and 125 | 1 |
| 112 and 50 | 2 |
| 43 and 108 | 1 |