Greatest Common Divisor (GCD) of 81 and 74
The greatest common divisor (GCD) of 81 and 74 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 74?
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 ÷ 74 = 1 remainder 7 |
| 2 | 74 ÷ 7 = 10 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 126 and 196 | 14 |
| 124 and 64 | 4 |
| 128 and 98 | 2 |
| 136 and 121 | 1 |
| 18 and 85 | 1 |