Greatest Common Divisor (GCD) of 96 and 180
The greatest common divisor (GCD) of 96 and 180 is 12.
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 96 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 | 96 ÷ 180 = 0 remainder 96 |
| 2 | 180 ÷ 96 = 1 remainder 84 |
| 3 | 96 ÷ 84 = 1 remainder 12 |
| 4 | 84 ÷ 12 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 146 and 38 | 2 |
| 32 and 190 | 2 |
| 127 and 55 | 1 |
| 11 and 151 | 1 |
| 64 and 147 | 1 |