Greatest Common Divisor (GCD) of 106 and 106
The greatest common divisor (GCD) of 106 and 106 is 106.
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 106 and 106?
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 | 106 ÷ 106 = 1 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 125 and 97 | 1 |
| 93 and 117 | 3 |
| 126 and 56 | 14 |
| 178 and 25 | 1 |
| 108 and 163 | 1 |