Greatest Common Divisor (GCD) of 90 and 154
The greatest common divisor (GCD) of 90 and 154 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 90 and 154?
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 | 90 ÷ 154 = 0 remainder 90 |
| 2 | 154 ÷ 90 = 1 remainder 64 |
| 3 | 90 ÷ 64 = 1 remainder 26 |
| 4 | 64 ÷ 26 = 2 remainder 12 |
| 5 | 26 ÷ 12 = 2 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 75 and 181 | 1 |
| 117 and 122 | 1 |
| 157 and 152 | 1 |
| 152 and 150 | 2 |
| 43 and 66 | 1 |