Greatest Common Divisor (GCD) of 135 and 143
The greatest common divisor (GCD) of 135 and 143 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 135 and 143?
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 ÷ 143 = 0 remainder 135 |
| 2 | 143 ÷ 135 = 1 remainder 8 |
| 3 | 135 ÷ 8 = 16 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 177 and 165 | 3 |
| 63 and 81 | 9 |
| 161 and 174 | 1 |
| 99 and 68 | 1 |
| 133 and 145 | 1 |