Greatest Common Divisor (GCD) of 110 and 180
The greatest common divisor (GCD) of 110 and 180 is 10.
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 110 and 180?
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 | 110 ÷ 180 = 0 remainder 110 |
| 2 | 180 ÷ 110 = 1 remainder 70 |
| 3 | 110 ÷ 70 = 1 remainder 40 |
| 4 | 70 ÷ 40 = 1 remainder 30 |
| 5 | 40 ÷ 30 = 1 remainder 10 |
| 6 | 30 ÷ 10 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 181 and 190 | 1 |
| 144 and 84 | 12 |
| 170 and 188 | 2 |
| 104 and 40 | 8 |
| 142 and 176 | 2 |