Greatest Common Divisor (GCD) of 25 and 150
The greatest common divisor (GCD) of 25 and 150 is 25.
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 25 and 150?
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 | 25 ÷ 150 = 0 remainder 25 |
| 2 | 150 ÷ 25 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 177 and 137 | 1 |
| 149 and 42 | 1 |
| 103 and 190 | 1 |
| 142 and 191 | 1 |
| 185 and 39 | 1 |