Greatest Common Divisor (GCD) of 190 and 118
The greatest common divisor (GCD) of 190 and 118 is 2.
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 190 and 118?
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 | 190 ÷ 118 = 1 remainder 72 |
| 2 | 118 ÷ 72 = 1 remainder 46 |
| 3 | 72 ÷ 46 = 1 remainder 26 |
| 4 | 46 ÷ 26 = 1 remainder 20 |
| 5 | 26 ÷ 20 = 1 remainder 6 |
| 6 | 20 ÷ 6 = 3 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 61 and 10 | 1 |
| 104 and 95 | 1 |
| 139 and 101 | 1 |
| 170 and 91 | 1 |
| 102 and 72 | 6 |