Greatest Common Divisor (GCD) of 77 and 99
The greatest common divisor (GCD) of 77 and 99 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 99?
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 ÷ 99 = 0 remainder 77 |
| 2 | 99 ÷ 77 = 1 remainder 22 |
| 3 | 77 ÷ 22 = 3 remainder 11 |
| 4 | 22 ÷ 11 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 59 and 146 | 1 |
| 182 and 160 | 2 |
| 89 and 192 | 1 |
| 137 and 193 | 1 |
| 135 and 38 | 1 |