Skill: factoring-gcf

Factoring with the GCF Practice

Find greatest common factors, pull them out completely, factor by grouping, and prove each answer by multiplying back.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss earns another hint; a third miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

GCF of numbers

The greatest divisor of both.

GCF(24, 36) → 12

GCF of monomials

gcd of coefficients, min exponent.

GCF(12x³, 18x²) → 6x²

Factor out the GCF

Divide every term by the GCF.

4x² + 8x → 4x(x + 2)

Factor by grouping

Pairs reveal a common binomial.

x³+2x²+3x+6 → (x+2)(x²+3)

Multiply back

Expand to verify a factorization.

3x²(2x+3) → 6x³+9x²

Fully factored?

Spot the factorization that stopped early.

2x(3x+6) → not done

3 Watch out for these

The three mistakes students make most often on these problems.

Stopping early

3x(2x² + 3x) still has an x inside — the GCF was 3x², not 3x.

Inventing a GCF

x² + 5 has GCF 1. The constant term must share the factor too.

Skipping the check

Multiply back every time — it catches sign and factor errors instantly.

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