Greatest Common Divisor (GCD) of 112 and 182
The greatest common divisor (GCD) of 112 and 182 is 14.
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 182?
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 ÷ 182 = 0 remainder 112 |
| 2 | 182 ÷ 112 = 1 remainder 70 |
| 3 | 112 ÷ 70 = 1 remainder 42 |
| 4 | 70 ÷ 42 = 1 remainder 28 |
| 5 | 42 ÷ 28 = 1 remainder 14 |
| 6 | 28 ÷ 14 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 156 and 141 | 3 |
| 166 and 36 | 2 |
| 75 and 17 | 1 |
| 184 and 155 | 1 |
| 105 and 93 | 3 |