Greatest Common Divisor (GCD) of 117 and 195
The greatest common divisor (GCD) of 117 and 195 is 39.
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 117 and 195?
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 | 117 ÷ 195 = 0 remainder 117 |
| 2 | 195 ÷ 117 = 1 remainder 78 |
| 3 | 117 ÷ 78 = 1 remainder 39 |
| 4 | 78 ÷ 39 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 132 and 162 | 6 |
| 64 and 163 | 1 |
| 141 and 183 | 3 |
| 190 and 28 | 2 |
| 180 and 58 | 2 |