Greatest Common Divisor (GCD) of 140 and 170
The greatest common divisor (GCD) of 140 and 170 is 10.
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 140 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 | 140 ÷ 170 = 0 remainder 140 |
| 2 | 170 ÷ 140 = 1 remainder 30 |
| 3 | 140 ÷ 30 = 4 remainder 20 |
| 4 | 30 ÷ 20 = 1 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 20 and 40 | 20 |
| 179 and 178 | 1 |
| 114 and 63 | 3 |
| 136 and 82 | 2 |
| 42 and 162 | 6 |