Greatest Common Divisor (GCD) of 59 and 71
The greatest common divisor (GCD) of 59 and 71 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 59 and 71?
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 | 59 ÷ 71 = 0 remainder 59 |
| 2 | 71 ÷ 59 = 1 remainder 12 |
| 3 | 59 ÷ 12 = 4 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 16 and 106 | 2 |
| 178 and 131 | 1 |
| 55 and 179 | 1 |
| 183 and 44 | 1 |
| 97 and 77 | 1 |