Greatest Common Divisor (GCD) of 188 and 110
The greatest common divisor (GCD) of 188 and 110 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 188 and 110?
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 | 188 ÷ 110 = 1 remainder 78 |
| 2 | 110 ÷ 78 = 1 remainder 32 |
| 3 | 78 ÷ 32 = 2 remainder 14 |
| 4 | 32 ÷ 14 = 2 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 39 and 87 | 3 |
| 21 and 103 | 1 |
| 44 and 113 | 1 |
| 138 and 56 | 2 |
| 196 and 182 | 14 |