Greatest Common Divisor (GCD) of 77 and 124
The greatest common divisor (GCD) of 77 and 124 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 77 and 124?
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 ÷ 124 = 0 remainder 77 |
| 2 | 124 ÷ 77 = 1 remainder 47 |
| 3 | 77 ÷ 47 = 1 remainder 30 |
| 4 | 47 ÷ 30 = 1 remainder 17 |
| 5 | 30 ÷ 17 = 1 remainder 13 |
| 6 | 17 ÷ 13 = 1 remainder 4 |
| 7 | 13 ÷ 4 = 3 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 131 and 26 | 1 |
| 141 and 151 | 1 |
| 191 and 74 | 1 |
| 165 and 46 | 1 |
| 16 and 149 | 1 |