Greatest Common Divisor (GCD) of 69 and 69
The greatest common divisor (GCD) of 69 and 69 is 69.
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 69 and 69?
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 | 69 ÷ 69 = 1 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 141 and 184 | 1 |
| 139 and 116 | 1 |
| 180 and 87 | 3 |
| 95 and 155 | 5 |
| 111 and 191 | 1 |