Greatest Common Divisor (GCD) of 120 and 182
The greatest common divisor (GCD) of 120 and 182 is 2.
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 182?
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 ÷ 182 = 0 remainder 120 |
| 2 | 182 ÷ 120 = 1 remainder 62 |
| 3 | 120 ÷ 62 = 1 remainder 58 |
| 4 | 62 ÷ 58 = 1 remainder 4 |
| 5 | 58 ÷ 4 = 14 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 168 and 37 | 1 |
| 197 and 82 | 1 |
| 130 and 133 | 1 |
| 107 and 54 | 1 |
| 54 and 129 | 3 |