Greatest Common Divisor (GCD) of 114 and 145
The greatest common divisor (GCD) of 114 and 145 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 114 and 145?
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 | 114 ÷ 145 = 0 remainder 114 |
| 2 | 145 ÷ 114 = 1 remainder 31 |
| 3 | 114 ÷ 31 = 3 remainder 21 |
| 4 | 31 ÷ 21 = 1 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 132 and 49 | 1 |
| 76 and 162 | 2 |
| 68 and 57 | 1 |
| 17 and 101 | 1 |
| 180 and 167 | 1 |