Greatest Common Divisor (GCD) of 135 and 154
The greatest common divisor (GCD) of 135 and 154 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 154?
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 ÷ 154 = 0 remainder 135 |
| 2 | 154 ÷ 135 = 1 remainder 19 |
| 3 | 135 ÷ 19 = 7 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 166 and 38 | 2 |
| 134 and 72 | 2 |
| 186 and 121 | 1 |
| 54 and 58 | 2 |
| 170 and 64 | 2 |