Greatest Common Divisor (GCD) of 546 and 310
The greatest common divisor (GCD) of 546 and 310 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 546 and 310?
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 | 546 ÷ 310 = 1 remainder 236 |
| 2 | 310 ÷ 236 = 1 remainder 74 |
| 3 | 236 ÷ 74 = 3 remainder 14 |
| 4 | 74 ÷ 14 = 5 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 74 and 52 | 2 |
| 99 and 113 | 1 |
| 38 and 17 | 1 |
| 134 and 105 | 1 |
| 112 and 197 | 1 |