
Greatest Common Divisor (GCD) of 89 and 77
The greatest common divisor (GCD) of 89 and 77 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 89 and 77?
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 | 89 ÷ 77 = 1 remainder 12 |
2 | 77 ÷ 12 = 6 remainder 5 |
3 | 12 ÷ 5 = 2 remainder 2 |
4 | 5 ÷ 2 = 2 remainder 1 |
5 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
Numbers | GCD |
---|---|
135 and 168 | 3 |
191 and 74 | 1 |
115 and 172 | 1 |
48 and 184 | 8 |
129 and 89 | 1 |