1. What is a Factor Pair?

A factor pair consists of two numbers that, when multiplied together, equal a given number. For example, the factor pairs of 12 are: (1, 12), (2, 6), (3, 4), (4, 3), (6, 2), and (12, 1).

2. How Does the Calculator Work?

The calculator uses the mathematical equation:

Where:

• \( a \) and \( b \) — Factors of the number
• \( n \) — The number to be factored (default: 12)

Explanation: The calculator finds all integer pairs (a, b) that satisfy the equation a × b = n, including both positive factor pairs.

3. Importance of Factor Pairs

Details: Understanding factor pairs is fundamental in mathematics, particularly in number theory, algebra, and problem-solving. Factor pairs help in simplifying fractions, finding common denominators, and solving equations.

4. Using the Calculator

Tips: Enter any positive integer to find its factor pairs. The calculator will display all possible combinations of two numbers that multiply to give your input number.

5. Frequently Asked Questions (FAQ)

Q1: What are the factor pairs of 12?
A: The factor pairs of 12 are: 1×12, 2×6, 3×4, 4×3, 6×2, and 12×1.

Q2: Does the order of factors matter?
A: Mathematically, a×b = b×a, so (3,4) and (4,3) are considered the same factor pair, though both are listed for completeness.

Q3: What about negative factors?
A: This calculator focuses on positive integer factors. Negative factors would follow the same pattern (e.g., -3 × -4 = 12).

Q4: Can I find factors of decimal numbers?
A: This calculator is designed for positive integers. Decimal numbers have infinite factor pairs.

Q5: What is the difference between factors and factor pairs?
A: Factors are the individual numbers that divide evenly into another number, while factor pairs are the specific pairs of factors that multiply together to equal the number.