Greatest Common Divisor (GCD) of 80 and 32
The greatest common divisor (GCD) of 80 and 32 is 16.
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 80 and 32?
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 | 80 ÷ 32 = 2 remainder 16 |
| 2 | 32 ÷ 16 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 109 and 119 | 1 |
| 169 and 15 | 1 |
| 135 and 120 | 15 |
| 105 and 84 | 21 |
| 190 and 155 | 5 |