Greatest Common Divisor (GCD) of 65 and 37
The greatest common divisor (GCD) of 65 and 37 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 65 and 37?
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 | 65 ÷ 37 = 1 remainder 28 |
| 2 | 37 ÷ 28 = 1 remainder 9 |
| 3 | 28 ÷ 9 = 3 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 120 and 26 | 2 |
| 125 and 125 | 125 |
| 182 and 141 | 1 |
| 94 and 158 | 2 |
| 148 and 66 | 2 |