Greatest Common Divisor (GCD) of 95 and 121
The greatest common divisor (GCD) of 95 and 121 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 95 and 121?
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 | 95 ÷ 121 = 0 remainder 95 |
| 2 | 121 ÷ 95 = 1 remainder 26 |
| 3 | 95 ÷ 26 = 3 remainder 17 |
| 4 | 26 ÷ 17 = 1 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 163 and 117 | 1 |
| 17 and 71 | 1 |
| 38 and 125 | 1 |
| 127 and 141 | 1 |
| 105 and 34 | 1 |