Greatest Common Divisor (GCD) of 980 and 868
The greatest common divisor (GCD) of 980 and 868 is 28.
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 980 and 868?
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 | 980 ÷ 868 = 1 remainder 112 |
| 2 | 868 ÷ 112 = 7 remainder 84 |
| 3 | 112 ÷ 84 = 1 remainder 28 |
| 4 | 84 ÷ 28 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 56 and 146 | 2 |
| 56 and 62 | 2 |
| 11 and 37 | 1 |
| 114 and 163 | 1 |
| 70 and 63 | 7 |