Greatest Common Divisor (GCD) of 48 and 88
The greatest common divisor (GCD) of 48 and 88 is 8.
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 88?
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 ÷ 88 = 0 remainder 48 |
| 2 | 88 ÷ 48 = 1 remainder 40 |
| 3 | 48 ÷ 40 = 1 remainder 8 |
| 4 | 40 ÷ 8 = 5 remainder 0 |
Examples of GCD Calculations
| Numbers | GCD |
|---|---|
| 146 and 44 | 2 |
| 158 and 20 | 2 |
| 172 and 79 | 1 |
| 144 and 84 | 12 |
| 109 and 168 | 1 |