Greatest Common Divisor (GCD) of 64 and 184
The greatest common divisor (GCD) of 64 and 184 is 8.
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 64 and 184?
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 | 64 ÷ 184 = 0 remainder 64 |
| 2 | 184 ÷ 64 = 2 remainder 56 |
| 3 | 64 ÷ 56 = 1 remainder 8 |
| 4 | 56 ÷ 8 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 110 and 155 | 5 |
| 165 and 169 | 1 |
| 197 and 101 | 1 |
| 183 and 113 | 1 |
| 182 and 164 | 2 |