Greatest Common Divisor (GCD) of 767 and 5
The greatest common divisor (GCD) of 767 and 5 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 767 and 5?
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 | 767 ÷ 5 = 153 remainder 2 |
| 2 | 5 ÷ 2 = 2 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 156 and 157 | 1 |
| 55 and 157 | 1 |
| 31 and 154 | 1 |
| 84 and 111 | 3 |
| 139 and 147 | 1 |