Greatest Common Divisor (GCD) of 132 and 187
The greatest common divisor (GCD) of 132 and 187 is 11.
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 132 and 187?
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 | 132 ÷ 187 = 0 remainder 132 |
| 2 | 187 ÷ 132 = 1 remainder 55 |
| 3 | 132 ÷ 55 = 2 remainder 22 |
| 4 | 55 ÷ 22 = 2 remainder 11 |
| 5 | 22 ÷ 11 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 193 and 197 | 1 |
| 110 and 196 | 2 |
| 12 and 14 | 2 |
| 36 and 60 | 12 |
| 50 and 172 | 2 |