Greatest Common Divisor (GCD) of 185 and 107
The greatest common divisor (GCD) of 185 and 107 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 185 and 107?
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 | 185 ÷ 107 = 1 remainder 78 |
| 2 | 107 ÷ 78 = 1 remainder 29 |
| 3 | 78 ÷ 29 = 2 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 160 and 41 | 1 |
| 94 and 163 | 1 |
| 46 and 32 | 2 |
| 106 and 198 | 2 |
| 63 and 130 | 1 |