A divisor of n is any integer that divides n evenly. To find all divisors, test numbers 1 through √n — for each divisor d, n/d is also a divisor. The number of divisors is τ(n), their sum is σ(n). A number is perfect if σ(n)−n = n (e.g., 6, 28, 496).
How to Use
Enter a positive integer:
- Divisors: Complete list
- Pairs: (d, n/d)
- Classification: Perfect/abundant/deficient
Special Numbers
- Perfect: σ(n)−n = n (6, 28, 496)
- Abundant: σ(n)−n > n (12, 18, 20)
- Deficient: σ(n)−n < n (most numbers)
Divisor Count
If n = p₁^a₁ × p₂^a₂ × ..., then τ(n) = (a₁+1)(a₂+1)... Powers of 2 have exactly n+1 divisors.
Step-by-Step Instructions
- 1Enter a positive integer.
- 2View all divisors.
- 3Check factor pairs.
- 4See divisor count and sum.
- 5Check perfect/abundant/deficient.