Greatest Common Divisor (GCD) of 89 and 167
The greatest common divisor (GCD) of 89 and 167 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 167?
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 ÷ 167 = 0 remainder 89 |
| 2 | 167 ÷ 89 = 1 remainder 78 |
| 3 | 89 ÷ 78 = 1 remainder 11 |
| 4 | 78 ÷ 11 = 7 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 60 and 70 | 10 |
| 28 and 139 | 1 |
| 120 and 108 | 12 |
| 154 and 23 | 1 |
| 45 and 168 | 3 |