Greatest Common Divisor (GCD) of 154 and 198
The greatest common divisor (GCD) of 154 and 198 is 22.
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 154 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 | 154 ÷ 198 = 0 remainder 154 |
| 2 | 198 ÷ 154 = 1 remainder 44 |
| 3 | 154 ÷ 44 = 3 remainder 22 |
| 4 | 44 ÷ 22 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 144 and 132 | 12 |
| 106 and 161 | 1 |
| 23 and 86 | 1 |
| 97 and 22 | 1 |
| 189 and 53 | 1 |