Factor Calculator
Solve Factor step by step — enter coefficients or expressions to get roots, factors, or simplified forms with detailed algebraic working.
Formula
n = p₁ᵃ × p₂ᵇ × ...
Any composite number can be written as a unique product of prime numbers.
Worked Examples
Example 1: Factors of 12
Problem:Find factors of 12
Solution:Pairs: 1×12, 2×6, 3×4.
Result:1, 2, 3, 4, 6, 12
Example 2: Prime Factors of 100
Problem:Factorize 100
Solution:100 = 10×10 = (2×5)×(2×5)
Result:2, 2, 5, 5
Frequently Asked Questions
Can a number have an odd number of factors?
Yes, only perfect squares (like 9, 16, 25) have an odd number of factors.
How do I check if a large number is prime?
You can use trial division up to the square root of the number. If no factors are found by then, it is prime.
Background & Theory
**Factors:**
Factors are integers that divide a number evenly (result is a whole number).
* Example: Factors of 10 are 1, 2, 5, 10.
**Prime Factorization:**
Breaking a number down into the set of prime numbers which multiply together to result in the original number.
* Example: 12 = 2 × 2 × 3
* This "fingerprint" is unique for every number.
**Prime Numbers:**
Numbers that have exactly two factors: 1 and themselves (e.g., 2, 3, 5, 7, 11).
**Composite Numbers:**
Numbers that have more than two factors.
History
The study of factors and prime numbers is a cornerstone of number theory, dating back to ancient Greece. Euclid (c. 300 BC) proved the fundamental theorem of arithmetic, which states that every integer greater than 1 is either a prime itself or can be represented as the product of prime numbers in a unique way.
Eratosthenes (c. 276-194 BC) created the "Sieve of Eratosthenes," a simple algorithm for finding all prime numbers up to a specified integer, which is still taught in schools today.