Greatest Common Divisor (GCD) of 283 and 909
The greatest common divisor (GCD) of 283 and 909 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 283 and 909?
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 | 283 ÷ 909 = 0 remainder 283 |
| 2 | 909 ÷ 283 = 3 remainder 60 |
| 3 | 283 ÷ 60 = 4 remainder 43 |
| 4 | 60 ÷ 43 = 1 remainder 17 |
| 5 | 43 ÷ 17 = 2 remainder 9 |
| 6 | 17 ÷ 9 = 1 remainder 8 |
| 7 | 9 ÷ 8 = 1 remainder 1 |
| 8 | 8 ÷ 1 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 124 and 65 | 1 |
| 18 and 117 | 9 |
| 178 and 12 | 2 |
| 151 and 175 | 1 |
| 197 and 41 | 1 |