Greatest Common Divisor (GCD) of 107 and 66
The greatest common divisor (GCD) of 107 and 66 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 107 and 66?
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 | 107 ÷ 66 = 1 remainder 41 |
| 2 | 66 ÷ 41 = 1 remainder 25 |
| 3 | 41 ÷ 25 = 1 remainder 16 |
| 4 | 25 ÷ 16 = 1 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 124 and 184 | 4 |
| 115 and 125 | 5 |
| 142 and 48 | 2 |
| 132 and 61 | 1 |
| 82 and 149 | 1 |