Greatest Common Divisor (GCD) of 127 and 163
The greatest common divisor (GCD) of 127 and 163 is 1.
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 127 and 163?
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 | 127 ÷ 163 = 0 remainder 127 |
| 2 | 163 ÷ 127 = 1 remainder 36 |
| 3 | 127 ÷ 36 = 3 remainder 19 |
| 4 | 36 ÷ 19 = 1 remainder 17 |
| 5 | 19 ÷ 17 = 1 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 186 and 98 | 2 |
| 177 and 39 | 3 |
| 120 and 145 | 5 |
| 149 and 132 | 1 |
| 48 and 145 | 1 |