Integer Divisor Counts and Signed Lists

Formula and method

Test positive divisors in complementary pairs up to the square root, then list them in ascending order. For two different integers, retain the positive divisors shared by both. Negative divisors are the negatives of the positive list.

An integer d ≠0 divides n when n=dq for an integer q.

Worked example

Enter these known values and leave the other values blank.

Assumptions and limitations

• Enter one or two integers with magnitude no greater than10000000000. A blank is absent, not zero. Only the two original inputs are editable.
• A single negative operand includes the original alternating positive/negative divisor list. Equal operands share one individual list; two different operands retain their own positive lists and common list.
• Zero has infinitely many nonzero divisors. Its finite list/count is withheld. One zero paired with a nonzero integer shares that integer’s finite positive divisors; two zeros remain unbounded.
• Each operand requires at most100000 divisor trials. The proved maximum2304positive divisors bounds the signed list and text sizes, so the browser never builds an arbitrary-size divisor list.
• Inputs accept decimal or e notation and bounded arithmetic expressions only when each intermediate and final value can be verified exactly as a finite decimal. Repeating fractions, functions, symbols and expressions that lose digits are rejected with guidance. Enter their finite decimal value instead; the calculator-specific magnitude and precision limits still apply.

Common questions

References

• Captured divisor controls and conditional lists/counts

Translate the captured divisor callback into the same bounded exact BigInt divisor kernel used by the isolated common-factor prototype. Preserve both optional original integer controls, single/equal/distinct operand branches, positive and signed divisor lists, counts and common-divisor explanations. Correct the zero callback case so it never publishes a finite list containing only zero or an invented finite zero count. No captured callback JavaScript is executed in product. Bind five numeric callback summaries and five declared plain-text lists to this complete divisor source/schema only. Accept integer magnitudes at most10000000000 with the proved100000-trial operand budget, maximum2304positive divisors and existing65536/250000character bounds. Zero has infinitely many nonzero divisors; a zero with a nonzero operand shares that operand’s positive divisors. Preserve either-optional-input UI/API readiness and all source conditional count/list contexts. Read only the two current validated operands, use the shared immutable eight-entry cache, and return only bounded numeric ASCII list text.

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• Decimal Rounding to the Nearest Hundredth
• Euclidean Residues and Signed Remainder Conventions
• Factor Lists and Common Divisors
• Floor: Round Down to an Integer