Greatest Common Divisor (GCD) of 76 and 114
The greatest common divisor (GCD) of 76 and 114 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 76 and 114?
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 | 76 ÷ 114 = 0 remainder 76 |
| 2 | 114 ÷ 76 = 1 remainder 38 |
| 3 | 76 ÷ 38 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 124 and 166 | 2 |
| 57 and 155 | 1 |
| 106 and 116 | 2 |
| 103 and 141 | 1 |
| 51 and 153 | 51 |