Greatest Common Divisor (GCD) of 45 and 85
The greatest common divisor (GCD) of 45 and 85 is 5.
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 45 and 85?
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 | 45 ÷ 85 = 0 remainder 45 |
| 2 | 85 ÷ 45 = 1 remainder 40 |
| 3 | 45 ÷ 40 = 1 remainder 5 |
| 4 | 40 ÷ 5 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 161 and 178 | 1 |
| 137 and 200 | 1 |
| 187 and 70 | 1 |
| 179 and 191 | 1 |
| 141 and 28 | 1 |