Greatest Common Divisor (GCD) of 171 and 133
The greatest common divisor (GCD) of 171 and 133 is 19.
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 171 and 133?
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 | 171 ÷ 133 = 1 remainder 38 |
| 2 | 133 ÷ 38 = 3 remainder 19 |
| 3 | 38 ÷ 19 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 15 and 114 | 3 |
| 110 and 157 | 1 |
| 45 and 160 | 5 |
| 161 and 193 | 1 |
| 98 and 106 | 2 |