Greatest Common Divisor (GCD) of 114 and 76
The greatest common divisor (GCD) of 114 and 76 is 38.
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 114 and 76?
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 | 114 ÷ 76 = 1 remainder 38 |
| 2 | 76 ÷ 38 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 18 and 196 | 2 |
| 195 and 152 | 1 |
| 158 and 124 | 2 |
| 122 and 46 | 2 |
| 185 and 111 | 37 |