Greatest Common Divisor (GCD) of 101 and 128
The greatest common divisor (GCD) of 101 and 128 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 101 and 128?
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 | 101 ÷ 128 = 0 remainder 101 |
| 2 | 128 ÷ 101 = 1 remainder 27 |
| 3 | 101 ÷ 27 = 3 remainder 20 |
| 4 | 27 ÷ 20 = 1 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 88 and 142 | 2 |
| 105 and 37 | 1 |
| 180 and 122 | 2 |
| 154 and 82 | 2 |
| 163 and 34 | 1 |