Greatest Common Divisor (GCD) of 811 and 763
The greatest common divisor (GCD) of 811 and 763 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 811 and 763?
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 | 811 ÷ 763 = 1 remainder 48 |
| 2 | 763 ÷ 48 = 15 remainder 43 |
| 3 | 48 ÷ 43 = 1 remainder 5 |
| 4 | 43 ÷ 5 = 8 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 104 and 144 | 8 |
| 149 and 54 | 1 |
| 128 and 27 | 1 |
| 35 and 61 | 1 |
| 162 and 165 | 3 |