Greatest Common Divisor (GCD) of 66 and 108
The greatest common divisor (GCD) of 66 and 108 is 6.
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 66 and 108?
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 | 66 ÷ 108 = 0 remainder 66 |
| 2 | 108 ÷ 66 = 1 remainder 42 |
| 3 | 66 ÷ 42 = 1 remainder 24 |
| 4 | 42 ÷ 24 = 1 remainder 18 |
| 5 | 24 ÷ 18 = 1 remainder 6 |
| 6 | 18 ÷ 6 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 72 and 27 | 9 |
| 74 and 95 | 1 |
| 180 and 81 | 9 |
| 149 and 186 | 1 |
| 197 and 93 | 1 |