Greatest Common Divisor (GCD) of 111 and 175
The greatest common divisor (GCD) of 111 and 175 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 111 and 175?
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 | 111 ÷ 175 = 0 remainder 111 |
| 2 | 175 ÷ 111 = 1 remainder 64 |
| 3 | 111 ÷ 64 = 1 remainder 47 |
| 4 | 64 ÷ 47 = 1 remainder 17 |
| 5 | 47 ÷ 17 = 2 remainder 13 |
| 6 | 17 ÷ 13 = 1 remainder 4 |
| 7 | 13 ÷ 4 = 3 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 113 and 195 | 1 |
| 77 and 110 | 11 |
| 134 and 92 | 2 |
| 38 and 106 | 2 |
| 81 and 149 | 1 |