Greatest Common Divisor (GCD) of 124 and 199
The greatest common divisor (GCD) of 124 and 199 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 124 and 199?
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 | 124 ÷ 199 = 0 remainder 124 |
| 2 | 199 ÷ 124 = 1 remainder 75 |
| 3 | 124 ÷ 75 = 1 remainder 49 |
| 4 | 75 ÷ 49 = 1 remainder 26 |
| 5 | 49 ÷ 26 = 1 remainder 23 |
| 6 | 26 ÷ 23 = 1 remainder 3 |
| 7 | 23 ÷ 3 = 7 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 110 and 20 | 10 |
| 77 and 191 | 1 |
| 132 and 170 | 2 |
| 42 and 84 | 42 |
| 184 and 150 | 2 |