Greatest Common Divisor (GCD) of 679 and 714
The greatest common divisor (GCD) of 679 and 714 is 7.
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 679 and 714?
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 | 679 ÷ 714 = 0 remainder 679 |
| 2 | 714 ÷ 679 = 1 remainder 35 |
| 3 | 679 ÷ 35 = 19 remainder 14 |
| 4 | 35 ÷ 14 = 2 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 63 and 166 | 1 |
| 97 and 21 | 1 |
| 148 and 153 | 1 |
| 40 and 107 | 1 |
| 163 and 155 | 1 |