Greatest Common Divisor (GCD) of 83 and 166
The greatest common divisor (GCD) of 83 and 166 is 83.
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 166?
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 ÷ 166 = 0 remainder 83 |
| 2 | 166 ÷ 83 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 57 and 110 | 1 |
| 186 and 116 | 2 |
| 137 and 123 | 1 |
| 118 and 72 | 2 |
| 21 and 181 | 1 |