Greatest Common Divisor (GCD) of 174 and 181
The greatest common divisor (GCD) of 174 and 181 is 1.
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 181?
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 ÷ 181 = 0 remainder 174 |
| 2 | 181 ÷ 174 = 1 remainder 7 |
| 3 | 174 ÷ 7 = 24 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 106 and 135 | 1 |
| 183 and 143 | 1 |
| 38 and 139 | 1 |
| 126 and 115 | 1 |
| 178 and 154 | 2 |