Greatest Common Divisor (GCD) of 184 and 67
The greatest common divisor (GCD) of 184 and 67 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 184 and 67?
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 | 184 ÷ 67 = 2 remainder 50 |
| 2 | 67 ÷ 50 = 1 remainder 17 |
| 3 | 50 ÷ 17 = 2 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 26 and 64 | 2 |
| 110 and 58 | 2 |
| 66 and 22 | 22 |
| 32 and 37 | 1 |
| 159 and 111 | 3 |