Greatest Common Divisor (GCD) of 95 and 149
The greatest common divisor (GCD) of 95 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 95 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 | 95 ÷ 149 = 0 remainder 95 |
| 2 | 149 ÷ 95 = 1 remainder 54 |
| 3 | 95 ÷ 54 = 1 remainder 41 |
| 4 | 54 ÷ 41 = 1 remainder 13 |
| 5 | 41 ÷ 13 = 3 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 57 and 105 | 3 |
| 153 and 33 | 3 |
| 155 and 188 | 1 |
| 50 and 185 | 5 |
| 100 and 107 | 1 |