Greatest Common Divisor (GCD) of 46 and 126
The greatest common divisor (GCD) of 46 and 126 is 2.
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 46 and 126?
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 | 46 ÷ 126 = 0 remainder 46 |
| 2 | 126 ÷ 46 = 2 remainder 34 |
| 3 | 46 ÷ 34 = 1 remainder 12 |
| 4 | 34 ÷ 12 = 2 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 148 and 106 | 2 |
| 191 and 146 | 1 |
| 56 and 55 | 1 |
| 196 and 105 | 7 |
| 53 and 41 | 1 |