Greatest Common Divisor (GCD) of 80 and 188
The greatest common divisor (GCD) of 80 and 188 is 4.
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 188?
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 ÷ 188 = 0 remainder 80 |
| 2 | 188 ÷ 80 = 2 remainder 28 |
| 3 | 80 ÷ 28 = 2 remainder 24 |
| 4 | 28 ÷ 24 = 1 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 170 and 24 | 2 |
| 184 and 161 | 23 |
| 100 and 92 | 4 |
| 76 and 142 | 2 |
| 132 and 139 | 1 |