Greatest Common Divisor (GCD) of 192 and 141
The greatest common divisor (GCD) of 192 and 141 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 192 and 141?
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 | 192 ÷ 141 = 1 remainder 51 |
| 2 | 141 ÷ 51 = 2 remainder 39 |
| 3 | 51 ÷ 39 = 1 remainder 12 |
| 4 | 39 ÷ 12 = 3 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 50 and 56 | 2 |
| 27 and 66 | 3 |
| 125 and 63 | 1 |
| 175 and 67 | 1 |
| 112 and 162 | 2 |