Greatest Common Divisor (GCD) of 153 and 198
The greatest common divisor (GCD) of 153 and 198 is 9.
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 153 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 | 153 ÷ 198 = 0 remainder 153 |
| 2 | 198 ÷ 153 = 1 remainder 45 |
| 3 | 153 ÷ 45 = 3 remainder 18 |
| 4 | 45 ÷ 18 = 2 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 189 and 34 | 1 |
| 135 and 16 | 1 |
| 154 and 115 | 1 |
| 26 and 120 | 2 |
| 89 and 31 | 1 |