Greatest Common Divisor (GCD) of 99 and 132
The greatest common divisor (GCD) of 99 and 132 is 33.
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 99 and 132?
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 | 99 ÷ 132 = 0 remainder 99 |
| 2 | 132 ÷ 99 = 1 remainder 33 |
| 3 | 99 ÷ 33 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 133 and 176 | 1 |
| 187 and 190 | 1 |
| 103 and 40 | 1 |
| 148 and 167 | 1 |
| 123 and 38 | 1 |