Factoring Calculator
Type a number to get its prime factorization and every factor pair, or enter a, b and c to factor a quadratic. Each answer comes with the steps written out the way you'd show them on homework.
Factor a Number
The factorization appears on the right as you type.
Factor a Quadratic: ax² + bx + c
Negative values are fine. Whole-number coefficients factor over the integers; decimals get exact roots instead.
Prime Factorization and the ac Method, Explained
A factoring calculator is only half useful if it hands you the answer without the route. Both tools on this page write out the work, so you can repeat the same moves on a test where it's just you and a pencil.
Prime factorization
Every whole number greater than 1 breaks into prime factors exactly one way. 360 equals 23 × 32 × 5, and no other combination of primes multiplies to 360. That guarantee (the fundamental theorem of arithmetic) is why prime factorization is the starting point for simplifying fractions, finding a greatest common factor, or reducing radicals.
Factor pairs
A factor pair is two numbers that multiply to your target. 36 has the pairs 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6. Once a pair repeats a number, you've found them all. The calculator lists every pair, so the one your problem wants is somewhere on the right.
Factoring quadratics with the ac method
To factor ax² + bx + c, multiply a and c, then hunt for two numbers that multiply to that product and add to b. For 2x² − 5x − 12: a·c = −24, and the pair 3 and −8 multiplies to −24 while adding to −5. Split the middle term into 3x − 8x, group the four terms in twos, factor each pair, and the shared binomial pops out: (2x + 3)(x − 4). The calculator shows exactly those numbers for your equation, so when a worksheet says "show the split", the split is right there.
When a quadratic will not factor
Check the discriminant, b² − 4ac. If it's a perfect square, the quadratic factors over the integers. If it's positive but not a perfect square, the roots are irrational, and you get them exactly as simplified radicals (√48 becomes 4√3) along with decimals. A negative discriminant means complex roots, and the calculator writes those out too. "Doesn't factor" never means "no answer".
Working on a line instead of a parabola? The slope calculator shows its substitution steps the same way.