Greatest Common Divisor (GCD) of 141 and 188
The greatest common divisor (GCD) of 141 and 188 is 47.
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 141 and 188?
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 | 141 ÷ 188 = 0 remainder 141 |
| 2 | 188 ÷ 141 = 1 remainder 47 |
| 3 | 141 ÷ 47 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 192 and 53 | 1 |
| 172 and 78 | 2 |
| 191 and 122 | 1 |
| 123 and 16 | 1 |
| 167 and 165 | 1 |