Greatest Common Divisor (GCD) of 128 and 175
The greatest common divisor (GCD) of 128 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 128 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 | 128 ÷ 175 = 0 remainder 128 |
| 2 | 175 ÷ 128 = 1 remainder 47 |
| 3 | 128 ÷ 47 = 2 remainder 34 |
| 4 | 47 ÷ 34 = 1 remainder 13 |
| 5 | 34 ÷ 13 = 2 remainder 8 |
| 6 | 13 ÷ 8 = 1 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 134 and 174 | 2 |
| 168 and 28 | 28 |
| 84 and 144 | 12 |
| 87 and 94 | 1 |
| 186 and 20 | 2 |