Greatest Common Divisor (GCD) of 170 and 196
The greatest common divisor (GCD) of 170 and 196 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 170 and 196?
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 | 170 ÷ 196 = 0 remainder 170 |
| 2 | 196 ÷ 170 = 1 remainder 26 |
| 3 | 170 ÷ 26 = 6 remainder 14 |
| 4 | 26 ÷ 14 = 1 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 125 and 66 | 1 |
| 45 and 164 | 1 |
| 60 and 178 | 2 |
| 94 and 49 | 1 |
| 104 and 130 | 26 |