Greatest Common Divisor (GCD) of 135 and 136
The greatest common divisor (GCD) of 135 and 136 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 136?
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 ÷ 136 = 0 remainder 135 |
| 2 | 136 ÷ 135 = 1 remainder 1 |
| 3 | 135 ÷ 1 = 135 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 144 and 157 | 1 |
| 153 and 160 | 1 |
| 25 and 103 | 1 |
| 115 and 87 | 1 |
| 72 and 12 | 12 |