Greatest Common Divisor (GCD) of 100 and 129
The greatest common divisor (GCD) of 100 and 129 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 100 and 129?
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 | 100 ÷ 129 = 0 remainder 100 |
| 2 | 129 ÷ 100 = 1 remainder 29 |
| 3 | 100 ÷ 29 = 3 remainder 13 |
| 4 | 29 ÷ 13 = 2 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 120 and 122 | 2 |
| 172 and 49 | 1 |
| 128 and 137 | 1 |
| 40 and 38 | 2 |
| 197 and 63 | 1 |