Greatest Common Divisor (GCD) of 94 and 149
The greatest common divisor (GCD) of 94 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 94 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 | 94 ÷ 149 = 0 remainder 94 |
| 2 | 149 ÷ 94 = 1 remainder 55 |
| 3 | 94 ÷ 55 = 1 remainder 39 |
| 4 | 55 ÷ 39 = 1 remainder 16 |
| 5 | 39 ÷ 16 = 2 remainder 7 |
| 6 | 16 ÷ 7 = 2 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 148 and 190 | 2 |
| 172 and 197 | 1 |
| 137 and 55 | 1 |
| 195 and 25 | 5 |
| 109 and 91 | 1 |