Greatest Common Divisor (GCD) of 143 and 198
The greatest common divisor (GCD) of 143 and 198 is 11.
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 143 and 198?
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 | 143 ÷ 198 = 0 remainder 143 |
| 2 | 198 ÷ 143 = 1 remainder 55 |
| 3 | 143 ÷ 55 = 2 remainder 33 |
| 4 | 55 ÷ 33 = 1 remainder 22 |
| 5 | 33 ÷ 22 = 1 remainder 11 |
| 6 | 22 ÷ 11 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 38 and 30 | 2 |
| 190 and 13 | 1 |
| 68 and 39 | 1 |
| 153 and 83 | 1 |
| 112 and 56 | 56 |