Greatest Common Divisor (GCD) of 118 and 163
The greatest common divisor (GCD) of 118 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 118 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 | 118 ÷ 163 = 0 remainder 118 |
| 2 | 163 ÷ 118 = 1 remainder 45 |
| 3 | 118 ÷ 45 = 2 remainder 28 |
| 4 | 45 ÷ 28 = 1 remainder 17 |
| 5 | 28 ÷ 17 = 1 remainder 11 |
| 6 | 17 ÷ 11 = 1 remainder 6 |
| 7 | 11 ÷ 6 = 1 remainder 5 |
| 8 | 6 ÷ 5 = 1 remainder 1 |
| 9 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 119 and 39 | 1 |
| 54 and 120 | 6 |
| 40 and 48 | 8 |
| 197 and 198 | 1 |
| 121 and 90 | 1 |