Greatest Common Divisor (GCD) of 176 and 199
The greatest common divisor (GCD) of 176 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 176 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 | 176 ÷ 199 = 0 remainder 176 |
| 2 | 199 ÷ 176 = 1 remainder 23 |
| 3 | 176 ÷ 23 = 7 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 132 and 125 | 1 |
| 69 and 185 | 1 |
| 180 and 148 | 4 |
| 153 and 167 | 1 |
| 120 and 97 | 1 |