Greatest Common Divisor (GCD) of 100 and 173
The greatest common divisor (GCD) of 100 and 173 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 173?
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 ÷ 173 = 0 remainder 100 |
| 2 | 173 ÷ 100 = 1 remainder 73 |
| 3 | 100 ÷ 73 = 1 remainder 27 |
| 4 | 73 ÷ 27 = 2 remainder 19 |
| 5 | 27 ÷ 19 = 1 remainder 8 |
| 6 | 19 ÷ 8 = 2 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 54 and 111 | 3 |
| 193 and 25 | 1 |
| 59 and 41 | 1 |
| 192 and 199 | 1 |
| 114 and 161 | 1 |