Greatest Common Divisor (GCD) of 677 and 952
The greatest common divisor (GCD) of 677 and 952 is 1.
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 677 and 952?
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 | 677 ÷ 952 = 0 remainder 677 |
| 2 | 952 ÷ 677 = 1 remainder 275 |
| 3 | 677 ÷ 275 = 2 remainder 127 |
| 4 | 275 ÷ 127 = 2 remainder 21 |
| 5 | 127 ÷ 21 = 6 remainder 1 |
| 6 | 21 ÷ 1 = 21 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 175 and 148 | 1 |
| 138 and 10 | 2 |
| 130 and 147 | 1 |
| 171 and 71 | 1 |
| 90 and 189 | 9 |