Greatest Common Divisor (GCD) of 183 and 106
The greatest common divisor (GCD) of 183 and 106 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 183 and 106?
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 | 183 ÷ 106 = 1 remainder 77 |
| 2 | 106 ÷ 77 = 1 remainder 29 |
| 3 | 77 ÷ 29 = 2 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 45 and 156 | 3 |
| 181 and 137 | 1 |
| 188 and 116 | 4 |
| 24 and 34 | 2 |
| 35 and 101 | 1 |