Greatest Common Divisor (GCD) of 77 and 131
The greatest common divisor (GCD) of 77 and 131 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 77 and 131?
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 | 77 ÷ 131 = 0 remainder 77 |
| 2 | 131 ÷ 77 = 1 remainder 54 |
| 3 | 77 ÷ 54 = 1 remainder 23 |
| 4 | 54 ÷ 23 = 2 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 153 and 84 | 3 |
| 68 and 182 | 2 |
| 162 and 167 | 1 |
| 167 and 131 | 1 |
| 171 and 173 | 1 |