Strengthen number sense with these divisibility rules worksheets. Students practice using rules for 2, 3, 4, 5, 6, 9, and 10, with a helpful first column for adding the digits of each number to check divisibility by 3 and 9. Understanding these rules makes it much easier to factor numbers and simplify fractions, giving learners a clearer path through more challenging math.
Use for the classroom or homeschool. Each worksheet includes an answer key.
Worksheet 1 Worksheet 2 Worksheet 3 Worksheet 4Divisibility rules help students quickly determine whether one number can be divided by another without leaving a remainder. This makes it easier to factor numbers, simplify fractions, and work more efficiently with larger values.
Understanding Divisibility Rules (Lesson)
By using these rules, you can decide if a number is divisible without doing long division.
- Divisible by 2: The number is even – it ends in 0, 2, 4, 6, or 8
- Divisible by 3: Add the digits: if the sum of the digits is divisible by 3, the number is divisible by 3
- Divisible by 4: The last two digits form a number divisible by 4
- Divisible by 5: The number ends in 0 or 5
- Divisible by 6: The number is divisible by both 2 and 3
- Divisible by 8: The last three digits form a number divisible by 8
- Divisible by 9: Add the digits: if the sum of the digits is divisible by 9, the number is divisible by 9
- Divisible by 10: The number ends in 0
Note:
If a number is not divisible by 2, then it is not divisible by 4, 6, 8 or 10.
If a number is not divisible by 3, then it is not divisible by 6 or 9.
Example: Check whether 1,368 is divisible by 2, 3, 4, 5, 6, 9, and 10.
Divisible by 2:
The number ends in 8, so 1,368 is divisible by 2.
Divisible by 3:
Add the digits: 1 + 3 + 6 + 8 = 18.
Since 18 is divisible by 3, 1,368 is divisible by 3.
Divisible by 4:
Look at the last two digits: 68.
Since 68 is divisible by 4, 1,368 is divisible by 4.
Divisible by 5:
The number does not end in 0 or 5, so 1,368 is not divisible by 5.
Divisible by 6:
A number must be divisible by both 2 and 3.
Since 1,368 meets both rules, it is divisible by 6.
Divisible by 9:
Use the digit sum again: 1 + 3 + 6 + 8 = 18.
Since 18 is divisible by 9, 1,368 is divisible by 9.
Divisible by 10:
The number does not end in 0, so 1,368 is not divisible by 10.
For More Divisibility Rules Printables
Download the divisibility rules with examples and an extra practice sheet from our workbook: Mastering Fractions with Factors and Multiples.
For more practice or help with other pre-algebra topics, try our workbooks.
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