Greatest Common Divisor (GCD) of 143 and 195
The greatest common divisor (GCD) of 143 and 195 is 13.
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 143 and 195?
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 | 143 ÷ 195 = 0 remainder 143 |
| 2 | 195 ÷ 143 = 1 remainder 52 |
| 3 | 143 ÷ 52 = 2 remainder 39 |
| 4 | 52 ÷ 39 = 1 remainder 13 |
| 5 | 39 ÷ 13 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 150 and 85 | 5 |
| 100 and 172 | 4 |
| 144 and 115 | 1 |
| 12 and 58 | 2 |
| 41 and 111 | 1 |