Analyze numbers through digits, factors, and sums. Spot Smith patterns, nearby matches, and explanations fast. Download clean reports and verify results with confidence today.
Enter a positive composite integer. Adjust the search radius to discover nearby Smith numbers around your input.
| Number | Prime Factors | Digit Sum | Factor Digit Sum | Smith Number? |
|---|---|---|---|---|
| 4 | 2 × 2 | 4 | 4 | Yes |
| 22 | 2 × 11 | 4 | 4 | Yes |
| 27 | 3 × 3 × 3 | 9 | 9 | Yes |
| 58 | 2 × 29 | 13 | 13 | Yes |
| 21 | 3 × 7 | 3 | 10 | No |
| 7 | Prime | 7 | Not applicable | No |
Digit Sum of the Number: S(n) = sum of every decimal digit in n.
Prime Factor Digit Sum: F(n) = sum of the digit sums of all prime factors, counted with multiplicity.
Smith Number Rule: A number is Smith when it is composite and S(n) = F(n).
Factorization Method: The calculator uses repeated division by prime candidates until the full prime factor list is produced.
A Smith number is a composite integer whose digit sum equals the combined digit sum of its prime factors, counted with multiplicity. Prime numbers do not qualify.
Yes. The digit sum of 4 is 4, and its prime factors are 2 and 2. Their digit sums add to 4, so it qualifies.
No. By definition, a Smith number must be composite. Even if a prime has the same digit sum as itself, it is excluded.
Multiplicity is part of the definition. For example, 27 factors as 3 × 3 × 3, so the digit sum of 3 is added three times.
No. This tool is designed for positive whole numbers only. Smith number testing starts with composite integers, so decimals and negatives are not valid inputs.
It scans numbers above and below your input within the chosen distance. The tool then lists nearby Smith numbers and sorts them by closeness.
Yes, but very large integers may take longer because prime factorization becomes more expensive as the number size increases.
The exports include the checked number, classification, digit sums, factorization, factor digit breakdown, selected radius, and nearby result count.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.