Greatest Common Divisor (GCD) of 103 and 198
The greatest common divisor (GCD) of 103 and 198 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 103 and 198?
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 | 103 ÷ 198 = 0 remainder 103 |
| 2 | 198 ÷ 103 = 1 remainder 95 |
| 3 | 103 ÷ 95 = 1 remainder 8 |
| 4 | 95 ÷ 8 = 11 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 159 and 35 | 1 |
| 112 and 121 | 1 |
| 102 and 89 | 1 |
| 47 and 199 | 1 |
| 38 and 24 | 2 |