Greatest Common Divisor (GCD) of 89 and 150
The greatest common divisor (GCD) of 89 and 150 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 89 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 | 89 ÷ 150 = 0 remainder 89 |
| 2 | 150 ÷ 89 = 1 remainder 61 |
| 3 | 89 ÷ 61 = 1 remainder 28 |
| 4 | 61 ÷ 28 = 2 remainder 5 |
| 5 | 28 ÷ 5 = 5 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 41 and 185 | 1 |
| 188 and 17 | 1 |
| 179 and 99 | 1 |
| 57 and 188 | 1 |
| 198 and 36 | 18 |