Greatest Common Divisor (GCD) of 77 and 175
The greatest common divisor (GCD) of 77 and 175 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 77 and 175?
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 | 77 ÷ 175 = 0 remainder 77 |
| 2 | 175 ÷ 77 = 2 remainder 21 |
| 3 | 77 ÷ 21 = 3 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 168 and 200 | 8 |
| 170 and 118 | 2 |
| 168 and 126 | 42 |
| 29 and 133 | 1 |
| 162 and 126 | 18 |