Greatest Common Divisor (GCD) of 195 and 142
The greatest common divisor (GCD) of 195 and 142 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 195 and 142?
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 | 195 ÷ 142 = 1 remainder 53 |
| 2 | 142 ÷ 53 = 2 remainder 36 |
| 3 | 53 ÷ 36 = 1 remainder 17 |
| 4 | 36 ÷ 17 = 2 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 144 and 68 | 4 |
| 175 and 195 | 5 |
| 132 and 73 | 1 |
| 133 and 124 | 1 |
| 137 and 122 | 1 |