Greatest Common Divisor (GCD) of 91 and 127
The greatest common divisor (GCD) of 91 and 127 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 91 and 127?
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 | 91 ÷ 127 = 0 remainder 91 |
| 2 | 127 ÷ 91 = 1 remainder 36 |
| 3 | 91 ÷ 36 = 2 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 |
|---|---|
| 73 and 89 | 1 |
| 119 and 150 | 1 |
| 187 and 40 | 1 |
| 178 and 90 | 2 |
| 129 and 61 | 1 |