Description
Compute one Legendre prime valuation contribution to n! trailing zeros for an explicitly supplied prime factor and base multiplicity; does not factor a base.
Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.
Compute one Legendre prime valuation contribution to n! trailing zeros for an explicitly supplied prime factor and base multiplicity; does not factor a base.
When to use this tool
Use Number: Factorial Trailing Zero Base Factor Term when you need this exact stated integer sign, bound, division, comparison, or factor component.
How to use the tool and how it works
- Enter factorialN, prime, basePrimeMultiplicity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
For factorialN in 0..1e9, candidate prime in 2..1e6, and basePrimeMultiplicity in 1..128 verify primality by trial division. Sum floor(N/prime^k) through repeated quotient division into primeValuation and return trailingZeroContribution=floor(valuation/multiplicity) inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| factorialN | Factorial N | Required. Safe integer. |
| prime | Prime | Required. Safe integer. |
| basePrimeMultiplicity | Base Prime Multiplicity | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.primeValuation | Prime Valuation | Calculated result member: number. |
| result.trailingZeroContribution | One prime factor's bound; full radix count takes the minimum across factors. | Calculated result member: number. |
{
"input": {
"factorialN": 10,
"prime": 5,
"basePrimeMultiplicity": 1
},
"output": {
"result": {
"primeValuation": 2,
"trailingZeroContribution": 2
}
}
}Limitations and assumptions
- This is one prime factor's trailing-zero bound for a radix. A complete radix result takes the minimum across all prime factors; factorial digits and a full base factorization are not computed.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.
References
Similar or alternative tools
- Prime Factorization One Exponent Contribution
Trial-divide candidate prime through its square root, reject a composite, then return factor=prime^exponent as exact decimal text.
- Positional Fraction Terminating Prime Support
Return remainingDenominator and terminating when it equals one.