Greatest Common Divisor (GCD) of 85 and 146
The greatest common divisor (GCD) of 85 and 146 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 85 and 146?
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 | 85 ÷ 146 = 0 remainder 85 |
| 2 | 146 ÷ 85 = 1 remainder 61 |
| 3 | 85 ÷ 61 = 1 remainder 24 |
| 4 | 61 ÷ 24 = 2 remainder 13 |
| 5 | 24 ÷ 13 = 1 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 78 and 53 | 1 |
| 148 and 98 | 2 |
| 33 and 25 | 1 |
| 142 and 128 | 2 |
| 82 and 63 | 1 |