Greatest Common Divisor (GCD) of 77 and 116
The greatest common divisor (GCD) of 77 and 116 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 77 and 116?
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 | 77 ÷ 116 = 0 remainder 77 |
| 2 | 116 ÷ 77 = 1 remainder 39 |
| 3 | 77 ÷ 39 = 1 remainder 38 |
| 4 | 39 ÷ 38 = 1 remainder 1 |
| 5 | 38 ÷ 1 = 38 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 122 and 138 | 2 |
| 161 and 123 | 1 |
| 61 and 138 | 1 |
| 173 and 86 | 1 |
| 14 and 80 | 2 |