Greatest Common Divisor (GCD) of 199 and 110
The greatest common divisor (GCD) of 199 and 110 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 199 and 110?
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 | 199 ÷ 110 = 1 remainder 89 |
| 2 | 110 ÷ 89 = 1 remainder 21 |
| 3 | 89 ÷ 21 = 4 remainder 5 |
| 4 | 21 ÷ 5 = 4 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 190 and 182 | 2 |
| 143 and 139 | 1 |
| 57 and 34 | 1 |
| 141 and 107 | 1 |
| 116 and 31 | 1 |