Greatest Common Divisor (GCD) of 120 and 192
The greatest common divisor (GCD) of 120 and 192 is 24.
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 120 and 192?
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 | 120 ÷ 192 = 0 remainder 120 |
| 2 | 192 ÷ 120 = 1 remainder 72 |
| 3 | 120 ÷ 72 = 1 remainder 48 |
| 4 | 72 ÷ 48 = 1 remainder 24 |
| 5 | 48 ÷ 24 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 149 and 84 | 1 |
| 27 and 53 | 1 |
| 93 and 93 | 93 |
| 61 and 18 | 1 |
| 183 and 27 | 3 |