Greatest Common Divisor (GCD) of 180 and 97
The greatest common divisor (GCD) of 180 and 97 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 180 and 97?
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 | 180 ÷ 97 = 1 remainder 83 |
| 2 | 97 ÷ 83 = 1 remainder 14 |
| 3 | 83 ÷ 14 = 5 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 183 and 188 | 1 |
| 199 and 182 | 1 |
| 67 and 124 | 1 |
| 114 and 35 | 1 |
| 120 and 10 | 10 |