Greatest Common Divisor (GCD) of 174 and 178
The greatest common divisor (GCD) of 174 and 178 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 174 and 178?
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 | 174 ÷ 178 = 0 remainder 174 |
| 2 | 178 ÷ 174 = 1 remainder 4 |
| 3 | 174 ÷ 4 = 43 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 128 and 151 | 1 |
| 186 and 163 | 1 |
| 180 and 180 | 180 |
| 109 and 119 | 1 |
| 119 and 110 | 1 |