Greatest Common Divisor (GCD) of 107 and 181
The greatest common divisor (GCD) of 107 and 181 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 181?
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 ÷ 181 = 0 remainder 107 |
| 2 | 181 ÷ 107 = 1 remainder 74 |
| 3 | 107 ÷ 74 = 1 remainder 33 |
| 4 | 74 ÷ 33 = 2 remainder 8 |
| 5 | 33 ÷ 8 = 4 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 134 and 107 | 1 |
| 117 and 151 | 1 |
| 138 and 59 | 1 |
| 195 and 164 | 1 |
| 164 and 158 | 2 |