Number Properties Explorer – Factors & More

The explorer profiles an integer across a dozen dimensions. Enter 12: it is even, composite (12 = 2²×3), has six divisors (1, 2, 3, 4, 6, 12) summing to 28, digit sum 3, and — as an excess of divisors — is highly composite, beaten below it only by 6. Enter 17: prime, odd, deficient (proper divisors sum to 1), digit sum 8. The tool shows prime factorization, divisor list and count, perfect/deficient/abundant classification, square/cube status (144 = 12²), binary and hexadecimal forms (12 = 1100₂ = C₁₆), and congruence classes (mod 3, 4, 5, 9). Cross-links between properties are flagged: divisible by 3 iff digit sum is; a square iff the divisor count is odd; perfect squares end in 0, 1, 4, 5, 6 or 9 in base 10.

1. 1

   Enter an integer

   Any whole number to profile

2. 2

   Scan divisors to √n

   Divisor list and count are generated

3. 3

   Classify

   Prime/composite, perfect/deficient/abundant, even/odd

4. 4

   Convert & cross-check

   Binary, hex, digit sums and divisibility tests appear together

• 1

  Squares have an odd number of divisors — 9 has three (1, 3, 9)

• 2

  Digit-sum rule: divisible by 3 ⇔ digit sum divisible by 3

• 3

  Perfect numbers satisfy σ(n) = 2n; 6 and 28 qualify

• Calling 1 prime or perfect — it is neither

• Counting n itself out of the divisor count when using σ conventions

• Assuming even numbers cannot be prime — 2 is

• Confusing digit sum (3 for 12) with digital root terminology