Greatest Common Divisor (GCD) of 159 and 102
The greatest common divisor (GCD) of 159 and 102 is 3.
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 159 and 102?
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 | 159 ÷ 102 = 1 remainder 57 |
| 2 | 102 ÷ 57 = 1 remainder 45 |
| 3 | 57 ÷ 45 = 1 remainder 12 |
| 4 | 45 ÷ 12 = 3 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 104 and 167 | 1 |
| 46 and 86 | 2 |
| 26 and 197 | 1 |
| 178 and 97 | 1 |
| 144 and 18 | 18 |