Greatest Common Divisor (GCD) of 189 and 173
The greatest common divisor (GCD) of 189 and 173 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 189 and 173?
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 | 189 ÷ 173 = 1 remainder 16 |
| 2 | 173 ÷ 16 = 10 remainder 13 |
| 3 | 16 ÷ 13 = 1 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 196 and 20 | 4 |
| 174 and 162 | 6 |
| 126 and 82 | 2 |
| 108 and 50 | 2 |
| 88 and 56 | 8 |