Greatest Common Divisor (GCD) of 179 and 118
The greatest common divisor (GCD) of 179 and 118 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 179 and 118?
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 | 179 ÷ 118 = 1 remainder 61 |
| 2 | 118 ÷ 61 = 1 remainder 57 |
| 3 | 61 ÷ 57 = 1 remainder 4 |
| 4 | 57 ÷ 4 = 14 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 181 and 197 | 1 |
| 136 and 146 | 2 |
| 185 and 103 | 1 |
| 113 and 19 | 1 |
| 166 and 122 | 2 |