Greatest Common Divisor (GCD) of 48 and 160
The greatest common divisor (GCD) of 48 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 48 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 | 48 ÷ 160 = 0 remainder 48 |
| 2 | 160 ÷ 48 = 3 remainder 16 |
| 3 | 48 ÷ 16 = 3 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 155 and 42 | 1 |
| 180 and 53 | 1 |
| 127 and 11 | 1 |
| 177 and 116 | 1 |
| 188 and 199 | 1 |