Greatest Common Divisor (GCD) of 191 and 140
The greatest common divisor (GCD) of 191 and 140 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 191 and 140?
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 | 191 ÷ 140 = 1 remainder 51 |
| 2 | 140 ÷ 51 = 2 remainder 38 |
| 3 | 51 ÷ 38 = 1 remainder 13 |
| 4 | 38 ÷ 13 = 2 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 154 and 195 | 1 |
| 113 and 81 | 1 |
| 153 and 67 | 1 |
| 177 and 69 | 3 |
| 160 and 58 | 2 |