Greatest Common Divisor (GCD) of 96 and 149
The greatest common divisor (GCD) of 96 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 96 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 | 96 ÷ 149 = 0 remainder 96 |
| 2 | 149 ÷ 96 = 1 remainder 53 |
| 3 | 96 ÷ 53 = 1 remainder 43 |
| 4 | 53 ÷ 43 = 1 remainder 10 |
| 5 | 43 ÷ 10 = 4 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 186 and 52 | 2 |
| 192 and 125 | 1 |
| 183 and 196 | 1 |
| 133 and 104 | 1 |
| 122 and 175 | 1 |