Greatest Common Divisor (GCD) of 144 and 160
The greatest common divisor (GCD) of 144 and 160 is 16.
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 144 and 160?
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 | 144 ÷ 160 = 0 remainder 144 |
| 2 | 160 ÷ 144 = 1 remainder 16 |
| 3 | 144 ÷ 16 = 9 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 146 and 168 | 2 |
| 149 and 199 | 1 |
| 109 and 144 | 1 |
| 35 and 54 | 1 |
| 196 and 45 | 1 |