Greatest Common Divisor (GCD) of 104 and 187
The greatest common divisor (GCD) of 104 and 187 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 187?
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 ÷ 187 = 0 remainder 104 |
| 2 | 187 ÷ 104 = 1 remainder 83 |
| 3 | 104 ÷ 83 = 1 remainder 21 |
| 4 | 83 ÷ 21 = 3 remainder 20 |
| 5 | 21 ÷ 20 = 1 remainder 1 |
| 6 | 20 ÷ 1 = 20 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 123 and 199 | 1 |
| 14 and 39 | 1 |
| 96 and 178 | 2 |
| 122 and 120 | 2 |
| 156 and 103 | 1 |