Greatest Common Divisor (GCD) of 81 and 148
The greatest common divisor (GCD) of 81 and 148 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 148?
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 ÷ 148 = 0 remainder 81 |
| 2 | 148 ÷ 81 = 1 remainder 67 |
| 3 | 81 ÷ 67 = 1 remainder 14 |
| 4 | 67 ÷ 14 = 4 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 130 and 137 | 1 |
| 177 and 176 | 1 |
| 191 and 52 | 1 |
| 146 and 162 | 2 |
| 163 and 67 | 1 |