Greatest Common Divisor (GCD) of 33 and 132
The greatest common divisor (GCD) of 33 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 33 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 | 33 ÷ 132 = 0 remainder 33 |
| 2 | 132 ÷ 33 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 148 and 151 | 1 |
| 103 and 137 | 1 |
| 124 and 90 | 2 |
| 120 and 184 | 8 |
| 156 and 73 | 1 |