Online Factor Calculator
Instantly find all factors, factor pairs, and the prime factorization of any positive integer. Perfect for math homework and simplifying fractions.
Understanding Factors
Master the basics of number theory and factorization.
Factor Pairs
Factors always come in pairs. When you find one factor, you automatically find another by seeing what you multiply it by to get the original number.
Prime Factorization
Every integer greater than 1 can be represented exactly one way as a product of prime numbers. This is known as the Fundamental Theorem of Arithmetic.
Why it Matters
Finding factors is essential for simplifying fractions, finding common denominators (LCM), and factoring polynomials in algebra.
Frequently Asked Questions
What is a factor?
A factor is a number that divides into another number exactly without leaving a remainder. For example, 3 is a factor of 12 because 12 divided by 3 is exactly 4.
What is prime factorization?
Prime factorization is finding which prime numbers multiply together to make the original number. It breaks down a composite number into its smallest "building blocks". For example, the prime factorization of 12 is 2 × 2 × 3 (or 2² × 3).
What is a prime number vs a composite number?
A prime number has exactly two distinct positive divisors: 1 and itself (e.g., 2, 3, 5, 7, 11). A composite number has more than two positive divisors (e.g., 4, 6, 8, 9, 10). The number 1 is considered neither prime nor composite.
How do you find all factors manually?
To find all factors, start by dividing the number by 1, then 2, then 3, and so on. If the division results in a whole number, both the divisor and the quotient form a "factor pair". You only need to check numbers up to the square root of your target number.
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