Greatest Common Divisor (GCD) of 79 and 141
The greatest common divisor (GCD) of 79 and 141 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 79 and 141?
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 | 79 ÷ 141 = 0 remainder 79 |
| 2 | 141 ÷ 79 = 1 remainder 62 |
| 3 | 79 ÷ 62 = 1 remainder 17 |
| 4 | 62 ÷ 17 = 3 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 124 and 192 | 4 |
| 32 and 200 | 8 |
| 14 and 18 | 2 |
| 25 and 67 | 1 |
| 96 and 196 | 4 |