Greatest Common Divisor (GCD) of 176 and 110
The greatest common divisor (GCD) of 176 and 110 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 176 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 | 176 ÷ 110 = 1 remainder 66 |
| 2 | 110 ÷ 66 = 1 remainder 44 |
| 3 | 66 ÷ 44 = 1 remainder 22 |
| 4 | 44 ÷ 22 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 34 and 102 | 34 |
| 132 and 94 | 2 |
| 22 and 149 | 1 |
| 160 and 68 | 4 |
| 106 and 123 | 1 |