Greatest Common Divisor (GCD) of 138 and 190
The greatest common divisor (GCD) of 138 and 190 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 138 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 | 138 ÷ 190 = 0 remainder 138 |
| 2 | 190 ÷ 138 = 1 remainder 52 |
| 3 | 138 ÷ 52 = 2 remainder 34 |
| 4 | 52 ÷ 34 = 1 remainder 18 |
| 5 | 34 ÷ 18 = 1 remainder 16 |
| 6 | 18 ÷ 16 = 1 remainder 2 |
| 7 | 16 ÷ 2 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 130 and 155 | 5 |
| 171 and 15 | 3 |
| 132 and 35 | 1 |
| 124 and 24 | 4 |
| 120 and 109 | 1 |