Greatest Common Divisor (GCD) of 77 and 44
The greatest common divisor (GCD) of 77 and 44 is 11.
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 44?
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 ÷ 44 = 1 remainder 33 |
| 2 | 44 ÷ 33 = 1 remainder 11 |
| 3 | 33 ÷ 11 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 117 and 143 | 13 |
| 189 and 99 | 9 |
| 127 and 23 | 1 |
| 192 and 138 | 6 |
| 197 and 197 | 197 |