Greatest Common Divisor (GCD) of 171 and 128
The greatest common divisor (GCD) of 171 and 128 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 171 and 128?
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 | 171 ÷ 128 = 1 remainder 43 |
| 2 | 128 ÷ 43 = 2 remainder 42 |
| 3 | 43 ÷ 42 = 1 remainder 1 |
| 4 | 42 ÷ 1 = 42 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 12 and 67 | 1 |
| 174 and 81 | 3 |
| 135 and 55 | 5 |
| 176 and 144 | 16 |
| 153 and 50 | 1 |