Greatest Common Divisor (GCD) of 124 and 176
The greatest common divisor (GCD) of 124 and 176 is 4.
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 124 and 176?
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 | 124 ÷ 176 = 0 remainder 124 |
| 2 | 176 ÷ 124 = 1 remainder 52 |
| 3 | 124 ÷ 52 = 2 remainder 20 |
| 4 | 52 ÷ 20 = 2 remainder 12 |
| 5 | 20 ÷ 12 = 1 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 143 and 56 | 1 |
| 106 and 196 | 2 |
| 197 and 53 | 1 |
| 65 and 104 | 13 |
| 197 and 160 | 1 |