Greatest Common Divisor (GCD) of 165 and 87
The greatest common divisor (GCD) of 165 and 87 is 3.
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 87?
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 ÷ 87 = 1 remainder 78 |
| 2 | 87 ÷ 78 = 1 remainder 9 |
| 3 | 78 ÷ 9 = 8 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 152 and 38 | 38 |
| 45 and 35 | 5 |
| 194 and 192 | 2 |
| 126 and 65 | 1 |
| 186 and 171 | 3 |