Greatest Common Divisor (GCD) of 88 and 189
The greatest common divisor (GCD) of 88 and 189 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 88 and 189?
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 | 88 ÷ 189 = 0 remainder 88 |
| 2 | 189 ÷ 88 = 2 remainder 13 |
| 3 | 88 ÷ 13 = 6 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 160 and 43 | 1 |
| 104 and 49 | 1 |
| 20 and 109 | 1 |
| 52 and 108 | 4 |
| 189 and 129 | 3 |