Number Factorization Calculator
Find all factors, prime factors, and factor pairs of a number.
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Analyze Numbers with our Factorization & Factorial Calculator
This tool provides a complete analysis of any integer, calculating its factorial (n!), finding all of its factors and factor pairs, and determining its prime factorization.
What is Number Factorization?
Number factorization is the process of breaking down a composite number into smaller integers that, when multiplied together, give you the original number. A related concept is the factorial (n!), which is the product of all positive integers up to that number. Our calculator provides a comprehensive analysis, including all factors, factor pairs, the prime factorization, and the factorial of the input number.
How It Works: Finding the Factors
The calculator uses efficient algorithms to analyze the number:
- Finding Factors: It iterates from 1 up to the square root of the number, checking for divisibility at each step.
- Prime Factorization: It repeatedly divides the number by the smallest prime numbers (2, 3, 5, etc.) until the number becomes 1.
- Factorial: It calculates the factorial using an iterative multiplication loop.
Frequently Asked Questions
What is a factorial of a number?
The factorial of a non-negative integer 'n', denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. The factorial of 0 is defined as 1.
How is a factorial used?
Factorials are used extensively in combinatorics and probability. They are the basis for calculating permutations (the number of ways to arrange items) and combinations (the number of ways to choose items).
What is the prime factorization of a number?
The prime factorization of a number is the process of finding which prime numbers multiply together to make the original number. For example, the prime factorization of 12 is 2 × 2 × 3. Our calculator provides this along with all other factors.
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