1. What is the Rectangle Factor?

The Rectangle Factor is the greatest common divisor (GCD) of a rectangle's length and width. It represents the largest common measurement that can evenly divide both dimensions of the rectangle.

2. How Does the Calculator Work?

The calculator uses the GCD formula:

Where:

• \( \text{Length} \) — The longer side of the rectangle
• \( \text{Width} \) — The shorter side of the rectangle

Explanation: The GCD is calculated using the Euclidean algorithm, which repeatedly divides the larger number by the smaller number until the remainder is zero.

3. Importance of Rectangle Factor

Details: The factor is useful in tiling problems, determining the largest square tiles that can perfectly cover a rectangular area without cutting, and in simplifying ratio problems involving rectangular dimensions.

4. Using the Calculator

Tips: Enter both length and width in the same units (e.g., both in meters or both in feet). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if my rectangle dimensions are decimals?
A: The calculator will first multiply by 100 to convert to integers, find the GCD, then divide by 100 to return the result.

Q2: What does a factor of 1 mean?
A: A factor of 1 means the length and width are co-prime (have no common divisors other than 1).

Q3: Can this be used for non-rectangular shapes?
A: The concept applies to any two numbers, but the geometric interpretation is specific to rectangles.

Q4: What's the relationship between factor and aspect ratio?
A: The factor helps simplify the aspect ratio to its most reduced form.

Q5: How is this different from the least common multiple?
A: GCD finds the largest common divisor, while LCM finds the smallest common multiple of the dimensions.