Greatest Common Divisor (GCD) of 180 and 61
The greatest common divisor (GCD) of 180 and 61 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 61?
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 ÷ 61 = 2 remainder 58 |
| 2 | 61 ÷ 58 = 1 remainder 3 |
| 3 | 58 ÷ 3 = 19 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 40 and 193 | 1 |
| 85 and 178 | 1 |
| 156 and 24 | 12 |
| 196 and 148 | 4 |
| 159 and 29 | 1 |