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Smith Number Checker

Enter a number to test the Smith property and see its prime factorisation.

How to use

  1. Enter your values in the fields above.
  2. Press Calculate to see your result instantly.
  3. Use the Share button to copy a link to your result.

About this calculator

A Smith number is a composite (non-prime) whole number whose digit sum equals the sum of the digits of its prime factors, counted with multiplicity, meaning each repeated prime factor is counted as many times as it appears. For example, 4 = 2 × 2 has digit sum 4, and its two prime factors each contribute a digit sum of 2, for a total of 4, so 4 qualifies; 22 = 2 × 11 has digit sum 4, and its factors 2 and 11 contribute 2 + (1+1) = 4 as well.

The name comes from a 1982 anecdote by mathematician Albert Wilansky, who noticed the property in his brother-in-law Harold Smith's telephone number, 493-7775. Smith numbers are a recreational number theory curiosity rather than a tool with practical applications, popular among puzzle enthusiasts and programming exercises that combine digit manipulation with prime factorisation.

This calculator factorises any composite number you enter, sums the digits of the number and of its prime factors, and tells you immediately whether it is a Smith number.

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