Greatest Common Divisor (GCD) of 168 and 190
The greatest common divisor (GCD) of 168 and 190 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 168 and 190?
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 | 168 ÷ 190 = 0 remainder 168 |
| 2 | 190 ÷ 168 = 1 remainder 22 |
| 3 | 168 ÷ 22 = 7 remainder 14 |
| 4 | 22 ÷ 14 = 1 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 67 and 185 | 1 |
| 112 and 14 | 14 |
| 178 and 147 | 1 |
| 89 and 63 | 1 |
| 161 and 10 | 1 |