Greatest Common Divisor (GCD) of 120 and 193
The greatest common divisor (GCD) of 120 and 193 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 120 and 193?
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 | 120 ÷ 193 = 0 remainder 120 |
| 2 | 193 ÷ 120 = 1 remainder 73 |
| 3 | 120 ÷ 73 = 1 remainder 47 |
| 4 | 73 ÷ 47 = 1 remainder 26 |
| 5 | 47 ÷ 26 = 1 remainder 21 |
| 6 | 26 ÷ 21 = 1 remainder 5 |
| 7 | 21 ÷ 5 = 4 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 156 and 84 | 12 |
| 115 and 73 | 1 |
| 19 and 17 | 1 |
| 104 and 64 | 8 |
| 145 and 47 | 1 |