Greatest Common Divisor (GCD) of 104 and 171
The greatest common divisor (GCD) of 104 and 171 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 104 and 171?
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 | 104 ÷ 171 = 0 remainder 104 |
| 2 | 171 ÷ 104 = 1 remainder 67 |
| 3 | 104 ÷ 67 = 1 remainder 37 |
| 4 | 67 ÷ 37 = 1 remainder 30 |
| 5 | 37 ÷ 30 = 1 remainder 7 |
| 6 | 30 ÷ 7 = 4 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 29 and 29 | 29 |
| 120 and 200 | 40 |
| 193 and 149 | 1 |
| 160 and 193 | 1 |
| 194 and 48 | 2 |