Greatest Common Divisor (GCD) of 197 and 113
The greatest common divisor (GCD) of 197 and 113 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 197 and 113?
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 | 197 ÷ 113 = 1 remainder 84 |
| 2 | 113 ÷ 84 = 1 remainder 29 |
| 3 | 84 ÷ 29 = 2 remainder 26 |
| 4 | 29 ÷ 26 = 1 remainder 3 |
| 5 | 26 ÷ 3 = 8 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 61 and 148 | 1 |
| 107 and 36 | 1 |
| 138 and 53 | 1 |
| 192 and 89 | 1 |
| 158 and 172 | 2 |