Enter any integer or polynomial expression into the Factoring Calculator to find all its factors and factor pairs. Type a number like 48 to get every factor pair, or a quadratic like x²+5x+4 to see it broken into binomial factors. Results show the complete factored form, all individual factors, and the total factor count — no sign-in needed. Also try the Math Solver (Step-by-Step).
Factored Form
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All Factors
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Factor Pairs
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Total Number of Factors
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Factoring is the process of breaking a number or expression down into a product of smaller numbers or simpler expressions that, when multiplied together, give the original value. For example, 12 factors into 3 × 4, and x²+5x+6 factors into (x+2)(x+3). See also our calculate Equation Solver Root 1 (x₁).
To factor a quadratic of the form x²+bx+c, find two numbers that add up to b and multiply to c. For x²+5x+4, the numbers 1 and 4 add to 5 and multiply to 4, so the factored form is (x+1)(x+4).
Factor pairs are two whole numbers that multiply together to produce the original number. For example, the factor pairs of 12 are (1,12), (2,6), and (3,4). Every factor appears in at least one pair.
Yes. For negative integers, the calculator returns both positive and negative factor pairs. For example, the factor pairs of -6 include (-2, 3) and (2, -3) because multiplying a negative and a positive number gives a negative result. You might also find our calculate Root x₁, Root x₂ & Discriminant (b² − 4ac) — Quadratic Formula useful.
Factors of a number include all whole numbers that divide it evenly, including 1 and the number itself. Prime factors are only the prime numbers in that list — numbers divisible only by 1 and themselves, such as 2, 3, 5, 7. For example, factors of 12 are 1, 2, 3, 4, 6, 12 while the prime factors are 2, 2, 3.
Type the polynomial using standard notation: use ^ for exponents (e.g. x^2 for x²), * for multiplication, and + or - for addition and subtraction. Examples: x^2+5x+6, 2x^2-8, x^2-9. Switch the Calculation Type to 'Polynomial Factoring' for these expressions.
A number can have any quantity of factors. Prime numbers have exactly 2 factors (1 and themselves), while highly composite numbers can have many. For instance, 48 has 10 factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
A number or expression is fully factored when it has been broken down into its most basic factor components that cannot be divided further. For integers this means expressing as a product of prime numbers. For polynomials it means writing as a product of irreducible binomials or monomials. Check out our calculate Parallel Line Equation, Shared Slope (a) & New Y-Intercept (b₂) — Parallel Line as well.