Greatest Common Divisor (GCD) of 142 and 185
The greatest common divisor (GCD) of 142 and 185 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 142 and 185?
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 | 142 ÷ 185 = 0 remainder 142 |
| 2 | 185 ÷ 142 = 1 remainder 43 |
| 3 | 142 ÷ 43 = 3 remainder 13 |
| 4 | 43 ÷ 13 = 3 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 72 and 153 | 9 |
| 171 and 90 | 9 |
| 181 and 176 | 1 |
| 191 and 39 | 1 |
| 149 and 128 | 1 |