Greatest Common Divisor (GCD) of 32 and 149
The greatest common divisor (GCD) of 32 and 149 is 1.
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 32 and 149?
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 | 32 ÷ 149 = 0 remainder 32 |
| 2 | 149 ÷ 32 = 4 remainder 21 |
| 3 | 32 ÷ 21 = 1 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 54 and 69 | 3 |
| 96 and 156 | 12 |
| 124 and 64 | 4 |
| 30 and 37 | 1 |
| 22 and 130 | 2 |