Greatest Common Divisor (GCD) of 103 and 163
The greatest common divisor (GCD) of 103 and 163 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 103 and 163?
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 | 103 ÷ 163 = 0 remainder 103 |
| 2 | 163 ÷ 103 = 1 remainder 60 |
| 3 | 103 ÷ 60 = 1 remainder 43 |
| 4 | 60 ÷ 43 = 1 remainder 17 |
| 5 | 43 ÷ 17 = 2 remainder 9 |
| 6 | 17 ÷ 9 = 1 remainder 8 |
| 7 | 9 ÷ 8 = 1 remainder 1 |
| 8 | 8 ÷ 1 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 159 and 169 | 1 |
| 19 and 114 | 19 |
| 179 and 190 | 1 |
| 193 and 24 | 1 |
| 138 and 127 | 1 |