Greatest Common Divisor (GCD) of 16 and 17
The greatest common divisor (GCD) of 16 and 17 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 16 and 17?
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 | 16 ÷ 17 = 0 remainder 16 |
| 2 | 17 ÷ 16 = 1 remainder 1 |
| 3 | 16 ÷ 1 = 16 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 144 and 178 | 2 |
| 153 and 144 | 9 |
| 113 and 20 | 1 |
| 46 and 182 | 2 |
| 100 and 82 | 2 |