How do you find the greatest common factor?

Take the largest number dividing every coefficient, and each shared variable at its lowest power. Multiply those together — that's the GCF.

Why factor out the GCF first?

It simplifies every later step. Most 'factor completely' problems expect the GCF pulled out before any trinomial or difference-of-squares pattern is applied.

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How is this different from IXL?

No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is double-checked for accuracy before it reaches you.

Algebra 2 practice

Factoring Out the GCF

Factoring out the greatest common factor is the first move in almost every factoring problem: $6x^3 + 9x^2 = 3x^2(2x + 3)$ . Below: how to find the GCF of coefficients and variables, the terms students leave behind, and practice with explained feedback.

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What you'll practice

The greatest common factor (GCF) is the largest expression that divides every term. Factoring it out first — $6x^3 + 9x^2 = 3x^2(2x + 3)$ — simplifies everything that follows, and forgetting it is the single most common reason "factor completely" answers get marked wrong. These questions cover numeric GCFs, variable GCFs, and both together.

Worked example

Factor $6x^3 + 9x^2$ .

Find the GCF of the coefficients: $\gcd(6, 9) = 3$ .
Find the GCF of the variables: $x^3$ and $x^2$ share $x^2$ (always the lowest power).
So the GCF is $3x^2$ . Divide each term by it: $6x^3 \div 3x^2 = 2x$ and $9x^2 \div 3x^2 = 3$ .
$6x^3 + 9x^2 = 3x^2(2x + 3)$ . Check by distributing. ✓

Common mistakes

Taking the highest power instead of the lowest: the GCF of $x^3$ and $x^2$ is $x^2$ , not $x^3$ .
Leaving a term behind: $8x^2 + 12x = 4x(2x + 3)$ — dividing $12x$ by $4x$ leaves $3$ , not $0$ .
Missing the full numeric GCF: $6x^3 + 9x^2 = 3x^2(2x+3)$ , not $x^2(6x+9)$ — the 3 belongs outside.

Try a few

1. Factor $8x^2 + 12x$ .

$4x(2x+3)$
$4(2x^2+3x)$
$2x(4x+6)$
$8x(x+12)$

2. Factor $5x^3 - 10x^2 + 15x$ .

$5x(x^2-2x+3)$
$5(x^3-2x^2+3x)$
$5x(x^2-10x+15)$
$x(5x^2-10x+15)$

3. Factor $14x^2y - 21xy^2$ .

$7xy(2x-3y)$
$7(2x^2y-3xy^2)$
$xy(14x-21y)$
$7xy(2x-3)$

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FAQ

How do you find the greatest common factor?: Take the largest number dividing every coefficient, and each shared variable at its lowest power. Multiply those together — that's the GCF.
Why factor out the GCF first?: It simplifies every later step. Most 'factor completely' problems expect the GCF pulled out before any trinomial or difference-of-squares pattern is applied.
Is Cramzoo free?: Cramzoo is free to start — every unit opens with free skills and no account is needed. This particular skill is part of Premium ($6/month or $30/year), which unlocks every skill plus the parent progress dashboard.
How is this different from IXL?: No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is double-checked for accuracy before it reaches you.

Related Algebra 2 skills

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