Greatest Common Divisor (GCD) of 56 and 94
The greatest common divisor (GCD) of 56 and 94 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 56 and 94?
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 | 56 ÷ 94 = 0 remainder 56 |
| 2 | 94 ÷ 56 = 1 remainder 38 |
| 3 | 56 ÷ 38 = 1 remainder 18 |
| 4 | 38 ÷ 18 = 2 remainder 2 |
| 5 | 18 ÷ 2 = 9 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 182 and 144 | 2 |
| 174 and 31 | 1 |
| 105 and 179 | 1 |
| 77 and 162 | 1 |
| 90 and 184 | 2 |