Factoring Calculator - Mathematical Calculations & Solutions
How It Works
Select Type
Choose number or quadratic
Enter Values
Input number or coefficients
Common Examples
Factoring Calculator
What is Factoring?
Breaking down numbers or expressions into their constituent factors or prime components.
Why Factor?
Essential for solving equations, simplifying expressions, and understanding mathematical relationships.
Applications
Algebra, number theory, cryptography, polynomial equations, and mathematical problem solving.
Calculation Table
| Input | Type | Factored Form | Method |
|---|---|---|---|
| 12 | Number | 2² × 3 | Prime factorization |
| x² - 4 | Quadratic | (x - 2)(x + 2) | Difference of squares |
| x² + 6x + 9 | Quadratic | (x + 3)² | Perfect square |
| 2x² - 8x + 6 | Quadratic | 2(x - 1)(x - 3) | Quadratic formula |
Frequently Asked Questions
What types of factoring does this calculator support?
The calculator supports number factoring (finding all factors and prime factorization) and quadratic expression factoring (ax² + bx + c).
How does prime factorization work?
Prime factorization breaks a number into its prime factors. For example, 12 = 2² × 3, showing that 12 is composed of two 2s and one 3.
What is the difference between factors and prime factors?
Factors are all numbers that divide evenly into a given number, while prime factors are only the prime numbers that multiply together to make the original number.
How does quadratic factoring work?
Quadratic factoring converts expressions like ax² + bx + c into factored form (x - r₁)(x - r₂) using the quadratic formula to find roots.
What are special factoring cases?
Special cases include difference of squares (a² - b² = (a-b)(a+b)) and perfect square trinomials (a² ± 2ab + b² = (a ± b)²).
What if a quadratic cannot be factored?
If the discriminant (b² - 4ac) is negative, the quadratic has complex roots and cannot be factored over real numbers.
What are the practical applications of factoring?
Factoring is used in solving equations, simplifying fractions, cryptography, finding GCD/LCM, and analyzing polynomial functions.