Factoring out the GCF worksheet

Pulling out the greatest common factor is the first step in almost every factoring problem, and it applies to any polynomial, not just trinomials. Every trinomial on this sheet is prime once the factor is out, so the GCF really is the final answer.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Factoring Out the GCF Date Period Factor out the greatest common factor. $55 a + 132$ $24 p^{3} + 56 p^{2}$ $7 m^{2} + 35 m + 49$ $42 r + 140$ $63 n^{3} + 56 n^{2}$ $9 b^{2} + 72 b + 99$ $16 n + 10$ $110 k^{3} + 100 k^{2}$ $9 a^{2} + 27 a + 99$ $52 n + 39$ $56 m^{4} + 42 m^{3}$ $7 v^{2} + 14 v + 21$ $35 x + 45$ $70 n^{4} + 40 n^{3}$ $9 b^{2} + 81 b + 90$ $42 x + 66$ $80 x^{4} + 88 x^{3}$ $7 b^{2} + 63 b + 70$ $15 a + 20$ $42 y^{3} + 70 y^{2}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Factoring Out the GCF

Date Period

Factor out the greatest common factor.

$55 a + 132$
$24 p^{3} + 56 p^{2}$
$7 m^{2} + 35 m + 49$
$42 r + 140$
$63 n^{3} + 56 n^{2}$
$9 b^{2} + 72 b + 99$
$16 n + 10$
$110 k^{3} + 100 k^{2}$
$9 a^{2} + 27 a + 99$
$52 n + 39$
$56 m^{4} + 42 m^{3}$
$7 v^{2} + 14 v + 21$
$35 x + 45$
$70 n^{4} + 40 n^{3}$
$9 b^{2} + 81 b + 90$
$42 x + 66$
$80 x^{4} + 88 x^{3}$
$7 b^{2} + 63 b + 70$
$15 a + 20$
$42 y^{3} + 70 y^{2}$



Sigma Prep · sigmaprep.io/worksheets Name Factoring Out the GCFAnswer keyVersion 1 Date Period Factor out the greatest common factor. $55 a + 132$ $11 (5 a + 12)$ $24 p^{3} + 56 p^{2}$ $8 p^{2} (3 p + 7)$ $7 m^{2} + 35 m + 49$ $7 (m^{2} + 5 m + 7)$ $42 r + 140$ $14 (3 r + 10)$ $63 n^{3} + 56 n^{2}$ $7 n^{2} (9 n + 8)$ $9 b^{2} + 72 b + 99$ $9 (b^{2} + 8 b + 11)$ $16 n + 10$ $2 (8 n + 5)$ $110 k^{3} + 100 k^{2}$ $10 k^{2} (11 k + 10)$ $9 a^{2} + 27 a + 99$ $9 (a^{2} + 3 a + 11)$ $52 n + 39$ $13 (4 n + 3)$ $56 m^{4} + 42 m^{3}$ $14 m^{3} (4 m + 3)$ $7 v^{2} + 14 v + 21$ $7 (v^{2} + 2 v + 3)$ $35 x + 45$ $5 (7 x + 9)$ $70 n^{4} + 40 n^{3}$ $10 n^{3} (7 n + 4)$ $9 b^{2} + 81 b + 90$ $9 (b^{2} + 9 b + 10)$ $42 x + 66$ $6 (7 x + 11)$ $80 x^{4} + 88 x^{3}$ $8 x^{3} (10 x + 11)$ $7 b^{2} + 63 b + 70$ $7 (b^{2} + 9 b + 10)$ $15 a + 20$ $5 (3 a + 4)$ $42 y^{3} + 70 y^{2}$ $14 y^{2} (3 y + 5)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Factoring Out the GCFAnswer keyVersion 1

Date Period

Factor out the greatest common factor.

$55 a + 132$ $11 (5 a + 12)$
$24 p^{3} + 56 p^{2}$ $8 p^{2} (3 p + 7)$
$7 m^{2} + 35 m + 49$ $7 (m^{2} + 5 m + 7)$
$42 r + 140$ $14 (3 r + 10)$
$63 n^{3} + 56 n^{2}$ $7 n^{2} (9 n + 8)$
$9 b^{2} + 72 b + 99$ $9 (b^{2} + 8 b + 11)$
$16 n + 10$ $2 (8 n + 5)$
$110 k^{3} + 100 k^{2}$ $10 k^{2} (11 k + 10)$
$9 a^{2} + 27 a + 99$ $9 (a^{2} + 3 a + 11)$
$52 n + 39$ $13 (4 n + 3)$
$56 m^{4} + 42 m^{3}$ $14 m^{3} (4 m + 3)$
$7 v^{2} + 14 v + 21$ $7 (v^{2} + 2 v + 3)$
$35 x + 45$ $5 (7 x + 9)$
$70 n^{4} + 40 n^{3}$ $10 n^{3} (7 n + 4)$
$9 b^{2} + 81 b + 90$ $9 (b^{2} + 9 b + 10)$
$42 x + 66$ $6 (7 x + 11)$
$80 x^{4} + 88 x^{3}$ $8 x^{3} (10 x + 11)$
$7 b^{2} + 63 b + 70$ $7 (b^{2} + 9 b + 10)$
$15 a + 20$ $5 (3 a + 4)$
$42 y^{3} + 70 y^{2}$ $14 y^{2} (3 y + 5)$

How to do these

$12 x^{3} + 8 x^{2}$

The numbers 12 and 8 share a factor of 4.
Both terms have at least x², so x² comes out too.
That leaves 3x and 2 inside.

The answer is $4 x^{2} (3 x + 2)$ .

Where students go wrong

Taking out a factor rather than the greatest one. Pulling 2 out of 12x³ + 8x² leaves 2(6x³ + 4x²), which is still factorable, so it is not finished. The other habit worth breaking is only looking at the numbers: the powers of x share a factor too.

Also called factoring out the greatest common factor, taking out a common factor or highest common factor.

What you can put on this worksheet

Two terms, number only: $42 v + 12$ → $6 (7 v + 2)$
Two terms sharing a variable: $25 v^{3} + 15 v^{2}$ → $5 v^{2} (5 v + 3)$
Three terms: $4 v^{2} + 28 v + 8$ → $4 (v^{2} + 7 v + 2)$

Questions about these worksheets

Yes. Every factoring out the gcf sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the factoring out the gcf questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: two terms, number only, two terms sharing a variable and three terms. Tick as many as you want and set how many of each, or let it spread them evenly.

Factoring out the GCF worksheet

Select your difficulty

Factoring Out the GCF

Factoring Out the GCFAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

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