Greatest Common Divisor (GCD) of 138 and 176
The greatest common divisor (GCD) of 138 and 176 is 2.
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 176?
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 ÷ 176 = 0 remainder 138 |
| 2 | 176 ÷ 138 = 1 remainder 38 |
| 3 | 138 ÷ 38 = 3 remainder 24 |
| 4 | 38 ÷ 24 = 1 remainder 14 |
| 5 | 24 ÷ 14 = 1 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 183 and 195 | 3 |
| 78 and 128 | 2 |
| 150 and 64 | 2 |
| 43 and 63 | 1 |
| 77 and 131 | 1 |