Greatest Common Divisor (GCD) of 154 and 99
The greatest common divisor (GCD) of 154 and 99 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 154 and 99?
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 ÷ 99 = 1 remainder 55 |
| 2 | 99 ÷ 55 = 1 remainder 44 |
| 3 | 55 ÷ 44 = 1 remainder 11 |
| 4 | 44 ÷ 11 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 109 and 163 | 1 |
| 151 and 58 | 1 |
| 106 and 46 | 2 |
| 124 and 199 | 1 |
| 195 and 80 | 5 |