Greatest Common Divisor (GCD) of 71 and 171
The greatest common divisor (GCD) of 71 and 171 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 71 and 171?
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 | 71 ÷ 171 = 0 remainder 71 |
| 2 | 171 ÷ 71 = 2 remainder 29 |
| 3 | 71 ÷ 29 = 2 remainder 13 |
| 4 | 29 ÷ 13 = 2 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 127 and 120 | 1 |
| 145 and 25 | 5 |
| 129 and 22 | 1 |
| 169 and 98 | 1 |
| 191 and 142 | 1 |