Greatest Common Divisor (GCD) of 136 and 177
The greatest common divisor (GCD) of 136 and 177 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 136 and 177?
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 | 136 ÷ 177 = 0 remainder 136 |
| 2 | 177 ÷ 136 = 1 remainder 41 |
| 3 | 136 ÷ 41 = 3 remainder 13 |
| 4 | 41 ÷ 13 = 3 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 165 and 36 | 3 |
| 119 and 186 | 1 |
| 39 and 104 | 13 |
| 108 and 171 | 9 |
| 105 and 102 | 3 |