Greatest Common Divisor (GCD) of 81 and 145
The greatest common divisor (GCD) of 81 and 145 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 81 and 145?
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 | 81 ÷ 145 = 0 remainder 81 |
| 2 | 145 ÷ 81 = 1 remainder 64 |
| 3 | 81 ÷ 64 = 1 remainder 17 |
| 4 | 64 ÷ 17 = 3 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 167 and 189 | 1 |
| 109 and 172 | 1 |
| 194 and 176 | 2 |
| 26 and 175 | 1 |
| 192 and 47 | 1 |