Divisibility rules worksheet for Pre-Algebra

By 2 if the last digit is even, by 5 if it ends in 0 or 5, by 10 if it ends in 0. By 3 if the digits add to a multiple of 3, by 9 if they add to a multiple of 9. By 4 if the last two digits make a multiple of 4, by 8 if the last three make a multiple of 8, and by 6 if it passes both 2 and 3.

Also taught in Algebra 1, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets Name Divisibility Rules Date Period Answer each question. Use divisibility tests Which of $2, 3, 5, 9, 10$ divide $5,680$ ? Which of $2, 3, 5, 9, 10$ divide $5,355$ ? Which of $2, 3, 5, 9, 10$ divide $1,608$ ? Which of $2, 3, 5, 9, 10$ divide $8,271$ ? Which of $2, 3, 5, 9, 10$ divide $1,047$ ? Which of $2, 3, 5, 9, 10$ divide $2,645$ ? Which of $2, 3, 5, 9, 10$ divide $6,840$ ? Which of $2, 3, 5, 9, 10$ divide $2,869$ ? Which of $2, 3, 5, 9, 10$ divide $9,345$ ? Which of $2, 3, 5, 9, 10$ divide $2,640$ ? Decide if it is divisible Is $3,529$ divisible by $10$ ? Is $8,958$ divisible by $6$ ? Is $4,610$ divisible by $5$ ? Is $8,359$ divisible by $4$ ? Is $6,292$ divisible by $9$ ? Is $9,828$ divisible by $3$ ? Is $8,683$ divisible by $2$ ? Is $8,192$ divisible by $8$ ? Is $5,692$ divisible by $10$ ? Is $8,838$ divisible by $2$ ? Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Divisibility Rules

Date Period

Answer each question.

Use divisibility tests
Which of $2, 3, 5, 9, 10$ divide $5,680$ ?
Which of $2, 3, 5, 9, 10$ divide $5,355$ ?
Which of $2, 3, 5, 9, 10$ divide $1,608$ ?
Which of $2, 3, 5, 9, 10$ divide $8,271$ ?
Which of $2, 3, 5, 9, 10$ divide $1,047$ ?
Which of $2, 3, 5, 9, 10$ divide $2,645$ ?
Which of $2, 3, 5, 9, 10$ divide $6,840$ ?
Which of $2, 3, 5, 9, 10$ divide $2,869$ ?
Which of $2, 3, 5, 9, 10$ divide $9,345$ ?
Which of $2, 3, 5, 9, 10$ divide $2,640$ ?

Decide if it is divisible
Is $3,529$ divisible by $10$ ?
Is $8,958$ divisible by $6$ ?
Is $4,610$ divisible by $5$ ?
Is $8,359$ divisible by $4$ ?
Is $6,292$ divisible by $9$ ?
Is $9,828$ divisible by $3$ ?
Is $8,683$ divisible by $2$ ?
Is $8,192$ divisible by $8$ ?
Is $5,692$ divisible by $10$ ?
Is $8,838$ divisible by $2$ ?



Sigma Prep · sigmaprep.io/worksheets Name Divisibility RulesAnswer keyVersion 1 Date Period Answer each question. Use divisibility tests Which of $2, 3, 5, 9, 10$ divide $5,680$ ? $2, 5, 10$ Which of $2, 3, 5, 9, 10$ divide $5,355$ ? $3, 5, 9$ Which of $2, 3, 5, 9, 10$ divide $1,608$ ? $2, 3$ Which of $2, 3, 5, 9, 10$ divide $8,271$ ? $3, 9$ Which of $2, 3, 5, 9, 10$ divide $1,047$ ? $3$ Which of $2, 3, 5, 9, 10$ divide $2,645$ ? $5$ Which of $2, 3, 5, 9, 10$ divide $6,840$ ? $2, 3, 5, 9, 10$ Which of $2, 3, 5, 9, 10$ divide $2,869$ ?None Which of $2, 3, 5, 9, 10$ divide $9,345$ ? $3, 5$ Which of $2, 3, 5, 9, 10$ divide $2,640$ ? $2, 3, 5, 10$ Decide if it is divisible Is $3,529$ divisible by $10$ ?No Is $8,958$ divisible by $6$ ?Yes Is $4,610$ divisible by $5$ ?Yes Is $8,359$ divisible by $4$ ?No Is $6,292$ divisible by $9$ ?No Is $9,828$ divisible by $3$ ?Yes Is $8,683$ divisible by $2$ ?No Is $8,192$ divisible by $8$ ?Yes Is $5,692$ divisible by $10$ ?No Is $8,838$ divisible by $2$ ?Yes Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Divisibility RulesAnswer keyVersion 1

Date Period

Answer each question.

Use divisibility tests
Which of $2, 3, 5, 9, 10$ divide $5,680$ ? $2, 5, 10$
Which of $2, 3, 5, 9, 10$ divide $5,355$ ? $3, 5, 9$
Which of $2, 3, 5, 9, 10$ divide $1,608$ ? $2, 3$
Which of $2, 3, 5, 9, 10$ divide $8,271$ ? $3, 9$
Which of $2, 3, 5, 9, 10$ divide $1,047$ ? $3$
Which of $2, 3, 5, 9, 10$ divide $2,645$ ? $5$
Which of $2, 3, 5, 9, 10$ divide $6,840$ ? $2, 3, 5, 9, 10$
Which of $2, 3, 5, 9, 10$ divide $2,869$ ?None
Which of $2, 3, 5, 9, 10$ divide $9,345$ ? $3, 5$
Which of $2, 3, 5, 9, 10$ divide $2,640$ ? $2, 3, 5, 10$

Decide if it is divisible
Is $3,529$ divisible by $10$ ?No
Is $8,958$ divisible by $6$ ?Yes
Is $4,610$ divisible by $5$ ?Yes
Is $8,359$ divisible by $4$ ?No
Is $6,292$ divisible by $9$ ?No
Is $9,828$ divisible by $3$ ?Yes
Is $8,683$ divisible by $2$ ?No
Is $8,192$ divisible by $8$ ?Yes
Is $5,692$ divisible by $10$ ?No
Is $8,838$ divisible by $2$ ?Yes

How to do these

$4,230$

It ends in 0: divisible by 2, 5 and 10.
The digits add to 9: divisible by 3 and 9, and so by 6.
30 is not a multiple of 4.

The answer is $2, 3, 5, 6, 9, 10$ .

Where students go wrong

Using the digit-sum rule for 4 or 6. The digit sum only works for 3 and 9; 4 looks at the last two digits and 6 needs both 2 and 3.

Also called divisibility rules, divisibility tests, divisible by 3 or divisible by 9.

What you can put on this worksheet

Divisibility tests: Which of $2, 3, 5, 10$ divide $745$ ? → $5$
Is it divisible?: Is $758$ divisible by $6$ ? → No

Questions about these worksheets

Yes. Every divisibility rules 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 divisibility rules 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 2: divisibility tests and is it divisible?. Tick as many as you want and set how many of each, or let it spread them evenly.

Using the digit-sum rule for 4 or 6. The digit sum only works for 3 and 9; 4 looks at the last two digits and 6 needs both 2 and 3.

Divisibility rules worksheet for Pre-Algebra

Select your difficulty

Use divisibility tests

Decide if it is divisible

Use divisibility tests

Decide if it is divisible

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these divisibility rules worksheets free?+

Do the divisibility rules worksheets come with an answer key?+

Are these divisibility rules worksheets printable?+

What grade are these divisibility rules worksheets for?+

Can I get a different version of the same divisibility rules worksheet?+

Is this a free alternative to Kuta Software for divisibility rules?+

Can I choose how hard the divisibility rules questions are?+

What kinds of question are on a divisibility rules worksheet?+

What do students get wrong with divisibility rules?+