Divisor Count Function Calculator

Factor n into prime powers and multiply one more than every exponent. Both one and n belong to the count, and tau(1) equals one. Inputs must be whole numbers inside the displayed safe bound. The calculator does not round decimals into the domain or silently substitute a different convention, so verify each entered integer before interpreting the exact result.

The result counts positive divisors including one and n; it does not enumerate or sum those divisors. The exponent-choice product can be checked by listing divisors for a smaller number with the same structure. Use the displayed factors, recurrence step, or modular residue as an independent check. Exact integer output means the implemented arithmetic has no decimal approximation within its bound; it does not prove an unrelated theorem or an unstated combinatorial model.

Exact trial factorization is bounded at one billion to keep browser execution predictable. The page does not attempt to enumerate huge divisor lists or factor arbitrary cryptographic-size values. The bound keeps browser work predictable and every returned integer within JavaScript's exact safe range. Larger inputs need arbitrary-precision software, explicit resource controls, and independent verification rather than treating an overflowed floating-point value as exact.