Find all factors of a number, factor pairs, and prime factorization, or use this factoring calculator for common algebraic expressions.
Your factors will appear here. Enter a value to get started.
Factor pairs
Prime factorization
Show how
How to find factors of a number
Factors divide a number evenly. For 20, test whole-number divisors to find 1, 2, 4, 5, 10, and 20.
What are factor pairs?
Factor pairs multiply to a number, such as 2 × 6 for 12. Each pair gives two factors without duplicating the reversed pair.
What is prime factorization?
Prime factorization writes a number as prime factors. For example, 60 = 2² × 3 × 5.
How to factor a quadratic
For a quadratic, find values that multiply to the leading coefficient times the constant and combine to make the middle coefficient.
How to factor an algebraic expression
Look for a greatest common factor, special patterns, quadratic factoring, or factor by grouping when two groups share the same binomial.
How to use it
Choose a number or expression
Use Number for factors and primes, or Expression for common algebraic factoring patterns.
Enter your value
Type a whole number or an expression such as x^2 + 5x + 6.
Read the result
See factors, pairs, prime factorization, or the factored expression and method used.
Questions
What are factors?
Factors are whole numbers that divide another whole number evenly.
What are factor pairs?
Factor pairs are two factors that multiply to the original number.
What are the factors of 20?
The positive factors of 20 are 1, 2, 4, 5, 10, and 20.
What are the factors of 30?
The positive factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
What is prime factorization?
Prime factorization writes a whole number as a product of prime numbers.
How do I find all factors of a number?
Test whole-number divisors from 1 up to the square root. Each divisor gives a matching factor pair.
Is 1 prime or composite?
No. The number 1 is neither prime nor composite.
What are the factors of 0?
Every non-zero integer divides 0, so 0 does not have a finite ordinary factor list.
What is the greatest common factor?
The greatest common factor is the largest factor shared by two or more terms or numbers.
How do you factor a quadratic?
Find values that multiply to the product of the leading and constant coefficients and add to the middle coefficient.
What is factoring by grouping?
Factoring by grouping rearranges terms into groups with a shared factor, then factors out the common binomial.
What is a difference of squares?
It is an expression such as x² − 9, which factors into two conjugate binomials: (x − 3)(x + 3).
Can this factor every expression?
No. It intentionally supports common integer-coefficient patterns and clearly says when an expression is outside those methods.
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