Greatest Common Divisor (GCD) of 73 and 111
The greatest common divisor (GCD) of 73 and 111 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 73 and 111?
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 | 73 ÷ 111 = 0 remainder 73 |
| 2 | 111 ÷ 73 = 1 remainder 38 |
| 3 | 73 ÷ 38 = 1 remainder 35 |
| 4 | 38 ÷ 35 = 1 remainder 3 |
| 5 | 35 ÷ 3 = 11 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 158 and 199 | 1 |
| 134 and 107 | 1 |
| 36 and 187 | 1 |
| 78 and 124 | 2 |
| 124 and 111 | 1 |