Greatest Common Divisor (GCD) of 112 and 196
The greatest common divisor (GCD) of 112 and 196 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 112 and 196?
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 | 112 ÷ 196 = 0 remainder 112 |
| 2 | 196 ÷ 112 = 1 remainder 84 |
| 3 | 112 ÷ 84 = 1 remainder 28 |
| 4 | 84 ÷ 28 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 184 and 51 | 1 |
| 29 and 11 | 1 |
| 179 and 113 | 1 |
| 73 and 119 | 1 |
| 43 and 189 | 1 |