Prime factorization worksheet

Every whole number above 1 is a product of primes in exactly one way. Split off the smallest prime that divides, keep going with what is left, and write repeats as powers. Listing factors is the same skill from the other side, and a monomial factors the same way with each letter written out.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Prime Factorization Date Period Answer each question. Find the prime factorization Find the prime factorization of $36$ . Find the prime factorization of $360$ . Find the prime factorization of $2,401$ . Find the prime factorization of $32$ . Find the prime factorization of $77$ . Decide if it is prime or composite Is $85$ prime or composite? Is $289$ prime or composite? Is $13$ prime or composite? Is $67$ prime or composite? Is $57$ prime or composite? List all the factors List all the factors of $105$ List all the factors of $25$ List all the factors of $74$ List all the factors of $163$ List all the factors of $18$ Factor the monomial completely Factor completely: $70 x^{3}$ Factor completely: $18 x y^{2}$ Factor completely: $147 x^{3} y$ Factor completely: $12 x$ Factor completely: $10 x y$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Prime Factorization

Date Period

Answer each question.

Find the prime factorization
Find the prime factorization of $36$ .
Find the prime factorization of $360$ .
Find the prime factorization of $2,401$ .
Find the prime factorization of $32$ .
Find the prime factorization of $77$ .

Decide if it is prime or composite
Is $85$ prime or composite?
Is $289$ prime or composite?
Is $13$ prime or composite?
Is $67$ prime or composite?
Is $57$ prime or composite?

List all the factors
List all the factors of $105$
List all the factors of $25$
List all the factors of $74$
List all the factors of $163$
List all the factors of $18$

Factor the monomial completely
Factor completely: $70 x^{3}$
Factor completely: $18 x y^{2}$
Factor completely: $147 x^{3} y$
Factor completely: $12 x$
Factor completely: $10 x y$



Sigma Prep · sigmaprep.io/worksheets Name Prime FactorizationAnswer keyVersion 1 Date Period Answer each question. Find the prime factorization Find the prime factorization of $36$ . $2^{2} \cdot 3^{2}$ Find the prime factorization of $360$ . $2^{3} \cdot 3^{2} \cdot 5$ Find the prime factorization of $2,401$ . $7^{4}$ Find the prime factorization of $32$ . $2^{5}$ Find the prime factorization of $77$ . $7 \cdot 11$ Decide if it is prime or composite Is $85$ prime or composite?Composite Is $289$ prime or composite?Composite Is $13$ prime or composite?Prime Is $67$ prime or composite?Prime Is $57$ prime or composite?Composite List all the factors List all the factors of $105$ $1, 3, 5, 7, 15, 21, 35, 105$ List all the factors of $25$ $1, 5, 25$ List all the factors of $74$ $1, 2, 37, 74$ List all the factors of $163$ $1, 163$ List all the factors of $18$ $1, 2, 3, 6, 9, 18$ Factor the monomial completely Factor completely: $70 x^{3}$ $2 \cdot 5 \cdot 7 \cdot x^{3}$ Factor completely: $18 x y^{2}$ $2 \cdot 3^{2} \cdot x \cdot y^{2}$ Factor completely: $147 x^{3} y$ $3 \cdot 7^{2} \cdot x^{3} \cdot y$ Factor completely: $12 x$ $2^{2} \cdot 3 \cdot x$ Factor completely: $10 x y$ $2 \cdot 5 \cdot x \cdot y$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Prime FactorizationAnswer keyVersion 1

Date Period

Answer each question.

Find the prime factorization
Find the prime factorization of $36$ . $2^{2} \cdot 3^{2}$
Find the prime factorization of $360$ . $2^{3} \cdot 3^{2} \cdot 5$
Find the prime factorization of $2,401$ . $7^{4}$
Find the prime factorization of $32$ . $2^{5}$
Find the prime factorization of $77$ . $7 \cdot 11$

Decide if it is prime or composite
Is $85$ prime or composite?Composite
Is $289$ prime or composite?Composite
Is $13$ prime or composite?Prime
Is $67$ prime or composite?Prime
Is $57$ prime or composite?Composite

List all the factors
List all the factors of $105$ $1, 3, 5, 7, 15, 21, 35, 105$
List all the factors of $25$ $1, 5, 25$
List all the factors of $74$ $1, 2, 37, 74$
List all the factors of $163$ $1, 163$
List all the factors of $18$ $1, 2, 3, 6, 9, 18$

Factor the monomial completely
Factor completely: $70 x^{3}$ $2 \cdot 5 \cdot 7 \cdot x^{3}$
Factor completely: $18 x y^{2}$ $2 \cdot 3^{2} \cdot x \cdot y^{2}$
Factor completely: $147 x^{3} y$ $3 \cdot 7^{2} \cdot x^{3} \cdot y$
Factor completely: $12 x$ $2^{2} \cdot 3 \cdot x$
Factor completely: $10 x y$ $2 \cdot 5 \cdot x \cdot y$

How to do these

Find the prime factorization of $360$

360 is 2 times 180, 180 is 2 times 90, 90 is 2 times 45.
45 is 3 times 15, and 15 is 3 times 5.
Three 2s, two 3s, one 5.

The answer is $2^{3} \cdot 3^{2} \cdot 5$ .

Where students go wrong

Stopping at a factor that is not prime. 360 = 8 times 45 is a factorization, but 8 and 45 are not primes, so it is not the prime factorization.

Also called factor trees, prime or composite or listing factors.

What you can put on this worksheet

Prime factorization: Find the prime factorization of $60$ . → $2^{2} \cdot 3 \cdot 5$
Prime or composite: Is $30$ prime or composite? → Composite
List every factor: List all the factors of $18$ → $1, 2, 3, 6, 9, 18$
Divisibility tests: Which of $2, 3, 5, 10$ divide $745$ ? → $5$
Factor a monomial completely: Factor completely: $50 x^{2}$ → $2 \cdot 5^{2} \cdot x^{2}$

Questions about these worksheets

Yes. Every prime factorization 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.

Pre-Algebra is usually taken around 7th or 8th 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 prime factorization 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 three 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 5: prime factorization, prime or composite, list every factor, divisibility tests and factor a monomial completely. Tick as many as you want and set how many of each, or let it spread them evenly.

Stopping at a factor that is not prime. 360 = 8 times 45 is a factorization, but 8 and 45 are not primes, so it is not the prime factorization.

Prime factorization worksheet

Find the prime factorization

Decide if it is prime or composite

List all the factors

Factor the monomial completely

Find the prime factorization

Decide if it is prime or composite

List all the factors

Factor the monomial completely

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these prime factorization worksheets free?+

Do the prime factorization worksheets come with an answer key?+

Are these prime factorization worksheets printable?+

What grade are these prime factorization worksheets for?+

Can I get a different version of the same prime factorization worksheet?+

Is this a free alternative to Kuta Software for prime factorization?+

Can I choose how hard the prime factorization questions are?+

What kinds of question are on a prime factorization worksheet?+

What do students get wrong with prime factorization?+