Greatest Common Divisor (GCD) of 103 and 149
The greatest common divisor (GCD) of 103 and 149 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 103 and 149?
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 | 103 ÷ 149 = 0 remainder 103 |
| 2 | 149 ÷ 103 = 1 remainder 46 |
| 3 | 103 ÷ 46 = 2 remainder 11 |
| 4 | 46 ÷ 11 = 4 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 114 and 23 | 1 |
| 188 and 91 | 1 |
| 86 and 110 | 2 |
| 124 and 132 | 4 |
| 79 and 37 | 1 |