Greatest Common Divisor (GCD) of 124 and 180
The greatest common divisor (GCD) of 124 and 180 is 4.
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 124 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 | 124 ÷ 180 = 0 remainder 124 |
| 2 | 180 ÷ 124 = 1 remainder 56 |
| 3 | 124 ÷ 56 = 2 remainder 12 |
| 4 | 56 ÷ 12 = 4 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 138 and 176 | 2 |
| 62 and 54 | 2 |
| 111 and 166 | 1 |
| 103 and 162 | 1 |
| 163 and 158 | 1 |