Greatest Common Divisor (GCD) of 175 and 103
The greatest common divisor (GCD) of 175 and 103 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 175 and 103?
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 | 175 ÷ 103 = 1 remainder 72 |
| 2 | 103 ÷ 72 = 1 remainder 31 |
| 3 | 72 ÷ 31 = 2 remainder 10 |
| 4 | 31 ÷ 10 = 3 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 137 and 120 | 1 |
| 121 and 56 | 1 |
| 127 and 65 | 1 |
| 141 and 46 | 1 |
| 193 and 162 | 1 |