Greatest Common Divisor (GCD) of 189 and 60
The greatest common divisor (GCD) of 189 and 60 is 3.
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 60?
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 ÷ 60 = 3 remainder 9 |
| 2 | 60 ÷ 9 = 6 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 156 and 90 | 6 |
| 50 and 27 | 1 |
| 145 and 76 | 1 |
| 121 and 147 | 1 |
| 80 and 194 | 2 |