Greatest Common Divisor (GCD) of 77 and 55
The greatest common divisor (GCD) of 77 and 55 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 55?
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 ÷ 55 = 1 remainder 22 |
| 2 | 55 ÷ 22 = 2 remainder 11 |
| 3 | 22 ÷ 11 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 50 and 171 | 1 |
| 172 and 139 | 1 |
| 159 and 36 | 3 |
| 134 and 151 | 1 |
| 188 and 172 | 4 |