Greatest Common Divisor (GCD) of 179 and 199
The greatest common divisor (GCD) of 179 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 179 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 | 179 ÷ 199 = 0 remainder 179 |
| 2 | 199 ÷ 179 = 1 remainder 20 |
| 3 | 179 ÷ 20 = 8 remainder 19 |
| 4 | 20 ÷ 19 = 1 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 176 and 66 | 22 |
| 181 and 130 | 1 |
| 111 and 62 | 1 |
| 150 and 122 | 2 |
| 159 and 88 | 1 |