Greatest Common Divisor (GCD) of 442 and 284
The greatest common divisor (GCD) of 442 and 284 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 442 and 284?
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 | 442 ÷ 284 = 1 remainder 158 |
| 2 | 284 ÷ 158 = 1 remainder 126 |
| 3 | 158 ÷ 126 = 1 remainder 32 |
| 4 | 126 ÷ 32 = 3 remainder 30 |
| 5 | 32 ÷ 30 = 1 remainder 2 |
| 6 | 30 ÷ 2 = 15 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 119 and 54 | 1 |
| 142 and 131 | 1 |
| 58 and 67 | 1 |
| 156 and 120 | 12 |
| 10 and 12 | 2 |