Greatest Common Divisor (GCD) of 120 and 199
The greatest common divisor (GCD) of 120 and 199 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 199?
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 ÷ 199 = 0 remainder 120 |
| 2 | 199 ÷ 120 = 1 remainder 79 |
| 3 | 120 ÷ 79 = 1 remainder 41 |
| 4 | 79 ÷ 41 = 1 remainder 38 |
| 5 | 41 ÷ 38 = 1 remainder 3 |
| 6 | 38 ÷ 3 = 12 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 157 and 16 | 1 |
| 92 and 31 | 1 |
| 60 and 98 | 2 |
| 31 and 21 | 1 |
| 153 and 85 | 17 |