Greatest Common Divisor (GCD) of 81 and 134
The greatest common divisor (GCD) of 81 and 134 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 81 and 134?
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 | 81 ÷ 134 = 0 remainder 81 |
| 2 | 134 ÷ 81 = 1 remainder 53 |
| 3 | 81 ÷ 53 = 1 remainder 28 |
| 4 | 53 ÷ 28 = 1 remainder 25 |
| 5 | 28 ÷ 25 = 1 remainder 3 |
| 6 | 25 ÷ 3 = 8 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 189 and 43 | 1 |
| 91 and 119 | 7 |
| 29 and 90 | 1 |
| 186 and 141 | 3 |
| 145 and 82 | 1 |