Greatest Common Divisor (GCD) of 165 and 15
The greatest common divisor (GCD) of 165 and 15 is 15.
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 165 and 15?
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 | 165 ÷ 15 = 11 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 109 and 14 | 1 |
| 65 and 73 | 1 |
| 134 and 65 | 1 |
| 114 and 195 | 3 |
| 71 and 156 | 1 |