Greatest Common Divisor (GCD) of 104 and 170
The greatest common divisor (GCD) of 104 and 170 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 104 and 170?
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 | 104 ÷ 170 = 0 remainder 104 |
| 2 | 170 ÷ 104 = 1 remainder 66 |
| 3 | 104 ÷ 66 = 1 remainder 38 |
| 4 | 66 ÷ 38 = 1 remainder 28 |
| 5 | 38 ÷ 28 = 1 remainder 10 |
| 6 | 28 ÷ 10 = 2 remainder 8 |
| 7 | 10 ÷ 8 = 1 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 110 and 116 | 2 |
| 134 and 78 | 2 |
| 21 and 54 | 3 |
| 142 and 138 | 2 |
| 70 and 184 | 2 |