Greatest Common Divisor (GCD) of 59 and 192
The greatest common divisor (GCD) of 59 and 192 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 59 and 192?
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 | 59 ÷ 192 = 0 remainder 59 |
| 2 | 192 ÷ 59 = 3 remainder 15 |
| 3 | 59 ÷ 15 = 3 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 104 and 122 | 2 |
| 36 and 65 | 1 |
| 181 and 174 | 1 |
| 140 and 50 | 10 |
| 146 and 119 | 1 |