Greatest Common Divisor (GCD) of 154 and 199
The greatest common divisor (GCD) of 154 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 154 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 | 154 ÷ 199 = 0 remainder 154 |
| 2 | 199 ÷ 154 = 1 remainder 45 |
| 3 | 154 ÷ 45 = 3 remainder 19 |
| 4 | 45 ÷ 19 = 2 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 25 and 200 | 25 |
| 55 and 36 | 1 |
| 77 and 97 | 1 |
| 120 and 164 | 4 |
| 41 and 186 | 1 |