Greatest Common Divisor (GCD) of 71 and 142
The greatest common divisor (GCD) of 71 and 142 is 71.
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 142?
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 ÷ 142 = 0 remainder 71 |
| 2 | 142 ÷ 71 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 141 and 190 | 1 |
| 133 and 37 | 1 |
| 136 and 78 | 2 |
| 146 and 53 | 1 |
| 124 and 56 | 4 |