Greatest Common Divisor (GCD) of 115 and 182
The greatest common divisor (GCD) of 115 and 182 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 115 and 182?
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 | 115 ÷ 182 = 0 remainder 115 |
| 2 | 182 ÷ 115 = 1 remainder 67 |
| 3 | 115 ÷ 67 = 1 remainder 48 |
| 4 | 67 ÷ 48 = 1 remainder 19 |
| 5 | 48 ÷ 19 = 2 remainder 10 |
| 6 | 19 ÷ 10 = 1 remainder 9 |
| 7 | 10 ÷ 9 = 1 remainder 1 |
| 8 | 9 ÷ 1 = 9 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 119 and 121 | 1 |
| 141 and 146 | 1 |
| 179 and 114 | 1 |
| 125 and 156 | 1 |
| 163 and 84 | 1 |