Greatest Common Divisor (GCD) of 179 and 64
The greatest common divisor (GCD) of 179 and 64 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 179 and 64?
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 | 179 ÷ 64 = 2 remainder 51 |
| 2 | 64 ÷ 51 = 1 remainder 13 |
| 3 | 51 ÷ 13 = 3 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 113 and 86 | 1 |
| 121 and 116 | 1 |
| 196 and 148 | 4 |
| 128 and 177 | 1 |
| 165 and 200 | 5 |