Greatest Common Divisor (GCD) of 138 and 175
The greatest common divisor (GCD) of 138 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 138 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 | 138 ÷ 175 = 0 remainder 138 |
| 2 | 175 ÷ 138 = 1 remainder 37 |
| 3 | 138 ÷ 37 = 3 remainder 27 |
| 4 | 37 ÷ 27 = 1 remainder 10 |
| 5 | 27 ÷ 10 = 2 remainder 7 |
| 6 | 10 ÷ 7 = 1 remainder 3 |
| 7 | 7 ÷ 3 = 2 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 166 and 96 | 2 |
| 73 and 163 | 1 |
| 113 and 100 | 1 |
| 179 and 94 | 1 |
| 81 and 78 | 3 |