Greatest Common Divisor (GCD) of 110 and 176
The greatest common divisor (GCD) of 110 and 176 is 22.
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 110 and 176?
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 | 110 ÷ 176 = 0 remainder 110 |
| 2 | 176 ÷ 110 = 1 remainder 66 |
| 3 | 110 ÷ 66 = 1 remainder 44 |
| 4 | 66 ÷ 44 = 1 remainder 22 |
| 5 | 44 ÷ 22 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 138 and 23 | 23 |
| 100 and 43 | 1 |
| 168 and 197 | 1 |
| 122 and 65 | 1 |
| 137 and 93 | 1 |