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Divisibility Rule Trace Checker
Check divisibility by 2 through 13 with complete arithmetic rule traces.
Signed integer with at most 100 digits
divisibility-rules.json
Browser only
Runs locally in your browser. Your files, pasted content and generated output are not uploaded. Reset clears this tool’s working data.
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How to use this tool
- Enter a signed decimal integer without spaces or exponent notation.
- Check all divisors from 2 through 13.
- Download the complete rules, signed trace expressions and magnitude quotient/remainder report.
Examples
For 203, the 7-rule trace uses 20 minus 2 times 3, giving 14, which is divisible by 7.
Limitations
- At most 100 magnitude digits, 2000 trace steps, 256 KiB output and 30 seconds.
- Uses only the explicit base-10 rules for divisors 2 through 13. Seven uses prefix minus twice the last digit; thirteen uses prefix plus four times the last digit, continuing on the absolute result.
- Quotients and nonnegative remainders describe the magnitude; the original sign is retained separately. Zero is divisible by every listed divisor. This is not general factorization.
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