Greatest Common Divisor (GCD) of 25 and 199
The greatest common divisor (GCD) of 25 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 25 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 | 25 ÷ 199 = 0 remainder 25 |
| 2 | 199 ÷ 25 = 7 remainder 24 |
| 3 | 25 ÷ 24 = 1 remainder 1 |
| 4 | 24 ÷ 1 = 24 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 138 and 90 | 6 |
| 113 and 45 | 1 |
| 180 and 53 | 1 |
| 116 and 182 | 2 |
| 122 and 73 | 1 |