Greatest Common Divisor (GCD) of 125 and 190
The greatest common divisor (GCD) of 125 and 190 is 5.
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 125 and 190?
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 | 125 ÷ 190 = 0 remainder 125 |
| 2 | 190 ÷ 125 = 1 remainder 65 |
| 3 | 125 ÷ 65 = 1 remainder 60 |
| 4 | 65 ÷ 60 = 1 remainder 5 |
| 5 | 60 ÷ 5 = 12 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 107 and 45 | 1 |
| 198 and 90 | 18 |
| 144 and 114 | 6 |
| 108 and 153 | 9 |
| 119 and 19 | 1 |