Examine the Number
Look at the last digit, the final two or three digits, and the sum of all digits.
Free Interactive Math Tool
Divisibility Rules Practice
Decide which divisibility rules apply to a whole number, examine the digits that control each rule, explain your reasoning, and confirm every result with exact division.
Learn How to Test Numbers Without Long Division
Learn how the last digit, digit sum, final two or three digits, and combinations of simpler rules can determine whether a whole number divides evenly.
Read the Divisibility Rules GuideHow It Works
Test Divisibility Step by Step
Examine the number, select every rule that applies, explain the evidence used by each rule, and confirm that the division leaves no remainder.
Select the Rules
Choose every listed divisor that divides the displayed number evenly.
Explain the Evidence
Use the relevant digits or connected rules to justify each divisibility decision.
Confirm by Division
Verify that each correct divisor produces a whole number with no remainder.
Interactive Practice
Divisibility Rules
Correct
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Problems
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Streak
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Test this whole number
378
Select every divisibility rule that applies to the displayed number.
1
Select Rules
2
Explain Why
3
Confirm Division
Practice Problem
Which divisibility rules apply?
Select every number below that divides 378 evenly with no remainder.
Step 2
Explain why each selected rule works.
Complete the reasoning for each correct divisibility rule. The exact prompts will change depending on the displayed number and the rules that apply.
Divisible by
Divisible by
Add all the digits.
Divisible by
Divisible by
Divisible by
11
Add alternating digits, then find the difference between the two sums.
First Group
Second Group
Step 3
Confirm with Division
Complete each division to verify that every selected rule divides the number evenly with no remainder.
Divide by
378 ÷ 6 =
remainder
Excellent!
You correctly identified every divisibility rule that applies.
Divisible by:
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Your rule explanations will appear here.
Helpful Strategies
Think Like a Mathematician
Look Before You Calculate
Most divisibility rules only require examining a few digits rather than performing long division.
Use Digit Sums
Divisibility by 3 and 9 depends entirely on the sum of the digits.
Build on Simpler Rules
Rules like 6 and 12 combine other divisibility rules, making them easier to remember.
Always Verify
A correct divisibility test means the remainder must be exactly zero.
Why Learn This?
Where Divisibility Rules Help
Prime Factorization
Quickly identify which prime numbers may divide a composite number before building a factor tree.
Simplifying Fractions
Recognize common factors of the numerator and denominator without testing every possible divisor.
Mental Math
Determine whether a division problem will produce a whole-number result before calculating the quotient.
Quick Reference
Common Divisibility Rules
Use these patterns to decide whether a number divides evenly without completing the full division first.
The last digit is even: 0, 2, 4, 6, or 8.
The sum of the digits is divisible by 3.
The number formed by the last two digits is divisible by 4.
The last digit is 0 or 5.
The number is divisible by both 2 and 3.
The number formed by the last three digits is divisible by 8.
The sum of the digits is divisible by 9.
The last digit is 0.
The difference between the alternating digit sums is 0 or a multiple of 11.
The number is divisible by both 3 and 4.
Keep Practicing Divisibility
Generate another number and practice recognizing divisibility patterns using digit-based reasoning and exact division.