Factor Calculator

1. Enter a positive integer up to 1,000,000. The default is 360, which has an interesting number of factors.
2. View all factors listed in sorted order. A factor is any integer that divides evenly into the number.
3. See the prime factorization: the number expressed as a product of prime numbers with exponents. For 360: 2³ × 3² × 5.
4. Check special properties: is the number prime? Is it a perfect number (where all its proper divisors sum to itself)?

Finding all factors of n:
  For each integer i from 1 to √n:
    If n ÷ i has no remainder, then i and n/i are both factors.

Prime factorization (trial division):
  Divide by 2 until odd, then by 3, 5, 7... up to √n.
  Example: 360
    360 ÷ 2 = 180
    180 ÷ 2 = 90
     90 ÷ 2 = 45
     45 ÷ 3 = 15
     15 ÷ 3 = 5
      5 is prime
  Result: 2^3 × 3^2 × 5

Number of factors from prime factorization:
  If n = p^a × q^b × r^c ...
  Number of factors = (a+1)(b+1)(c+1)...
  Example: 360 = 2^3 × 3^2 × 5^1
  Count = (3+1)(2+1)(1+1) = 4×3×2 = 24 factors

Perfect number: sum of proper divisors = n
  6 = 1+2+3, so 6 is perfect
  28 = 1+2+4+7+14, so 28 is perfect