Greatest Common Divisor (GCD) of 154 and 34
The greatest common divisor (GCD) of 154 and 34 is 2.
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 154 and 34?
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 | 154 ÷ 34 = 4 remainder 18 |
| 2 | 34 ÷ 18 = 1 remainder 16 |
| 3 | 18 ÷ 16 = 1 remainder 2 |
| 4 | 16 ÷ 2 = 8 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 179 and 89 | 1 |
| 122 and 153 | 1 |
| 181 and 158 | 1 |
| 61 and 168 | 1 |
| 146 and 46 | 2 |