Greatest Common Divisor (GCD) of 100 and 178
The greatest common divisor (GCD) of 100 and 178 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 100 and 178?
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 ÷ 178 = 0 remainder 100 |
| 2 | 178 ÷ 100 = 1 remainder 78 |
| 3 | 100 ÷ 78 = 1 remainder 22 |
| 4 | 78 ÷ 22 = 3 remainder 12 |
| 5 | 22 ÷ 12 = 1 remainder 10 |
| 6 | 12 ÷ 10 = 1 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 33 and 191 | 1 |
| 156 and 28 | 4 |
| 55 and 68 | 1 |
| 184 and 83 | 1 |
| 154 and 138 | 2 |