Greatest Common Divisor (GCD) of 168 and 103
The greatest common divisor (GCD) of 168 and 103 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 168 and 103?
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 | 168 ÷ 103 = 1 remainder 65 |
| 2 | 103 ÷ 65 = 1 remainder 38 |
| 3 | 65 ÷ 38 = 1 remainder 27 |
| 4 | 38 ÷ 27 = 1 remainder 11 |
| 5 | 27 ÷ 11 = 2 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 91 and 117 | 13 |
| 112 and 85 | 1 |
| 110 and 123 | 1 |
| 78 and 35 | 1 |
| 47 and 190 | 1 |