Greatest Common Divisor (GCD) of 145 and 183
The greatest common divisor (GCD) of 145 and 183 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 145 and 183?
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 | 145 ÷ 183 = 0 remainder 145 |
| 2 | 183 ÷ 145 = 1 remainder 38 |
| 3 | 145 ÷ 38 = 3 remainder 31 |
| 4 | 38 ÷ 31 = 1 remainder 7 |
| 5 | 31 ÷ 7 = 4 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 99 and 52 | 1 |
| 97 and 77 | 1 |
| 115 and 160 | 5 |
| 117 and 21 | 3 |
| 112 and 170 | 2 |