Factoring Calculator: Prime Factors & Polynomials With Steps
Factor whole numbers into prime factors with step-by-step division, exponent form, factor pairs, or factor quadratic polynomials.
Quick 1-Click Factoring Scenarios
Number or Algebraic Polynomial Input
Prime Factor Exponent Multiplicity
Count of times each prime base divides 360.
All Factor Pairs for 360
Pairs of integers whose product equals 360.
Step-by-Step Trial Division Ladder
Successive divisions by smallest primes until quotient equals 1.
| Step | Division Operation | Remaining Quotient |
|---|---|---|
| Step #1 | 360 ÷ 2 = 180 | 180 |
| Step #2 | 180 ÷ 2 = 90 | 90 |
| Step #3 | 90 ÷ 2 = 45 | 45 |
| Step #4 | 45 ÷ 3 = 15 | 15 |
| Step #5 | 15 ÷ 3 = 5 | 5 |
| Step #6 | 5 ÷ 5 = 1 | 1 |
Worked Example: Prime Factorization of 360
Breaking down the integer 360 by iterative prime trial division:
💡 Mathematical Theorem: 360 is completely factored into 2³ × 3² × 5. It possesses 24 positive divisors and 12 symmetric factor pairs ranging from 1 × 360 to 18 × 20.
Frequently Asked Questions
Authoritative Mathematics & Number Theory References
Rigorous mathematical reference on trial division, sieve of Eratosthenes, and the Fundamental Theorem of Arithmetic.
Comprehensive lessons on algebraic factoring methods, difference of squares, and grouping.
Mathematical standards on divisor functions, prime counts, and prime distribution.
Educational frameworks for teaching prime factor trees and algebraic factorization.
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AlgebraQuick Tips
- 1Double-check your input values for accuracy
- 2Use the correct units of measurement
- 3Round results to appropriate decimal places
- 4Consider the context when interpreting results