piapia123
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Number Facts

Convert

Everything runs locally in your browser — nothing is uploaded

Input
Drop a file here to load its contents
Output

One integer per line (large and negative values are fine), and a set of properties comes out at once: divisor structure (how many divisors, and their sum), the digital root and cross-sum, whether it is perfect, deficient or abundant, whether it is automorphic, a Harshad number, or a palindrome (with the previous and next palindromes), and its digit count in binary, octal, decimal and hexadecimal. Note that the Chinese term “cross-sum” is simply the repeated sum of the digits down to one digit, which is exactly the digital root; the interface shows both names so neither is mistaken for a separate quantity. ⚠️ Factorising large numbers has a trial-division cap. A twenty-digit semiprime cannot be factored within it, and the tool says plainly that trial division reached the cap without finding a factor, rather than stalling the page or inventing a divisor count. Prime factorisation itself lives in the Prime Numbers tool and is not repeated here. Everything runs locally in your browser; nothing is uploaded.

Features

  • Number of divisors and their sum (prime factorisation itself lives in the Prime Numbers tool)
  • Digital root and cross-sum, explained as the same thing
  • Perfect, deficient and abundant classification
  • Automorphic (5² = 25 still ends in 5) and Harshad (divisible by its digit sum) tests
  • Palindrome test, with the previous and next palindromes
  • Digit counts in binary, octal, decimal and hexadecimal
  • The base for the digital root can be switched (10, 16 or 2)
  • Trial division has a cap, and gives up honestly instead of stalling
  • Negatives are handled by absolute value, and the edge cases of 0 are stated
  • Everything runs locally in your browser; nothing is uploaded

How to use

  1. Enter one integer per line (thousands separators, large values and negatives are fine)
  2. Choose the base for the digital root (10, 16 or 2)
  3. Turn the number trivia off if you do not need it
  4. The result appears as you type, and every row can be copied

FAQ

Are the “cross-sum” and the “digital root” different?
They are the same thing. The cross-sum adds the digits of a number and repeats until one digit remains, which is exactly the definition of the digital root. Both names are shown so that either usage matches up.
Why can some large numbers not have a divisor count?
Because trial division has a cap. Counting divisors requires a complete factorisation, and a twenty-digit semiprime (the product of two ten-digit primes) will not yield a factor within it. Once the cap is reached the tool uses Miller-Rabin to test whether the remainder is prime, and if it is not, says plainly that the divisor structure is unknown instead of stalling. For a full factorisation, use the Prime Numbers tool.
Why does this tool not do prime factorisation?
Because the Prime Numbers tool already does it thoroughly (powers form plus each prime factor, using Pollard rho). Writing it twice would let the two drift apart with no test to catch it, so this tool only covers the properties that one does not.
How are negative numbers handled?
Palindromes, the digital root, automorphic and Harshad tests and digit counts all use the absolute value, and say so. The divisor count and sum are likewise for the absolute value. Zero is special: every non-zero integer divides it (infinitely many divisors), while perfect and Harshad are defined only for positive integers.

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