Greatest Common Divisor (GCD) of 135 and 20
The greatest common divisor (GCD) of 135 and 20 is 5.
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 20?
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 ÷ 20 = 6 remainder 15 |
| 2 | 20 ÷ 15 = 1 remainder 5 |
| 3 | 15 ÷ 5 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 185 and 149 | 1 |
| 143 and 45 | 1 |
| 141 and 151 | 1 |
| 117 and 52 | 13 |
| 105 and 84 | 21 |