Greatest Common Divisor (GCD) of 83 and 136
The greatest common divisor (GCD) of 83 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 83 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 | 83 ÷ 136 = 0 remainder 83 |
| 2 | 136 ÷ 83 = 1 remainder 53 |
| 3 | 83 ÷ 53 = 1 remainder 30 |
| 4 | 53 ÷ 30 = 1 remainder 23 |
| 5 | 30 ÷ 23 = 1 remainder 7 |
| 6 | 23 ÷ 7 = 3 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 176 and 71 | 1 |
| 55 and 195 | 5 |
| 157 and 144 | 1 |
| 198 and 144 | 18 |
| 188 and 42 | 2 |