Greatest Common Divisor (GCD) of 104 and 149
The greatest common divisor (GCD) of 104 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 104 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 | 104 ÷ 149 = 0 remainder 104 |
| 2 | 149 ÷ 104 = 1 remainder 45 |
| 3 | 104 ÷ 45 = 2 remainder 14 |
| 4 | 45 ÷ 14 = 3 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 155 and 31 | 31 |
| 110 and 86 | 2 |
| 127 and 99 | 1 |
| 166 and 153 | 1 |
| 39 and 42 | 3 |