Greatest Common Divisor (GCD) of 35 and 81
The greatest common divisor (GCD) of 35 and 81 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 35 and 81?
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 | 35 ÷ 81 = 0 remainder 35 |
| 2 | 81 ÷ 35 = 2 remainder 11 |
| 3 | 35 ÷ 11 = 3 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 189 and 75 | 3 |
| 169 and 97 | 1 |
| 103 and 117 | 1 |
| 164 and 70 | 2 |
| 185 and 19 | 1 |