Greatest Common Divisor (GCD) of 27 and 141
The greatest common divisor (GCD) of 27 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 27 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 | 27 ÷ 141 = 0 remainder 27 |
| 2 | 141 ÷ 27 = 5 remainder 6 |
| 3 | 27 ÷ 6 = 4 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 96 and 11 | 1 |
| 134 and 163 | 1 |
| 132 and 147 | 3 |
| 128 and 32 | 32 |
| 100 and 75 | 25 |