Factor Finder

How integer factors and classifications work

Factors (or divisors) of an integer are positive integers that divide the number evenly (without leaving a remainder). E.g. the factors of 12 are 1, 2, 3, 4, 6, and 12. Summing up proper divisors (all divisors excluding the number itself) lets us classify integers into three standard mathematical categories:

• Perfect Number: The sum of proper divisors equals the number itself (e.g. \(28 = 1 + 2 + 4 + 7 + 14\)).
• Abundant Number: The sum of proper divisors exceeds the number (e.g. for 12, proper sum is \(1+2+3+4+6 = 16 > 12\)).
• Deficient Number: The sum of proper divisors is less than the number (e.g. for 10, proper sum is \(1+2+5 = 8 < 10\)).