Greatest Common Divisor (GCD) of 28 and 56
The greatest common divisor (GCD) of 28 and 56 is 28.
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 28 and 56?
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 | 28 ÷ 56 = 0 remainder 28 |
| 2 | 56 ÷ 28 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 153 and 125 | 1 |
| 140 and 28 | 28 |
| 170 and 134 | 2 |
| 174 and 105 | 3 |
| 163 and 13 | 1 |