Greatest Common Divisor (GCD) of 135 and 90
The greatest common divisor (GCD) of 135 and 90 is 45.
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 135 and 90?
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 | 135 ÷ 90 = 1 remainder 45 |
| 2 | 90 ÷ 45 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 166 and 93 | 1 |
| 82 and 169 | 1 |
| 16 and 102 | 2 |
| 111 and 198 | 3 |
| 119 and 122 | 1 |