Greatest Common Divisor (GCD) of 133 and 174
The greatest common divisor (GCD) of 133 and 174 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 133 and 174?
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 | 133 ÷ 174 = 0 remainder 133 |
| 2 | 174 ÷ 133 = 1 remainder 41 |
| 3 | 133 ÷ 41 = 3 remainder 10 |
| 4 | 41 ÷ 10 = 4 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 38 and 42 | 2 |
| 162 and 163 | 1 |
| 25 and 46 | 1 |
| 103 and 126 | 1 |
| 26 and 33 | 1 |