Greatest Common Divisor (GCD) of 137 and 197
The greatest common divisor (GCD) of 137 and 197 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 137 and 197?
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 | 137 ÷ 197 = 0 remainder 137 |
| 2 | 197 ÷ 137 = 1 remainder 60 |
| 3 | 137 ÷ 60 = 2 remainder 17 |
| 4 | 60 ÷ 17 = 3 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 176 and 55 | 11 |
| 139 and 73 | 1 |
| 160 and 115 | 5 |
| 140 and 82 | 2 |
| 104 and 121 | 1 |