Factor Calculator
Break any positive integer down completely: every divisor, the matching factor pairs, the full prime factorization and a classification (prime, perfect square, perfect, abundant or deficient).
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Divisors of 36
9 divisors
1, 2, 3, 4, 6, 9, 12, 18, 36
- Number
- 36
- Divisor count
- 9
- Prime factorization
- 2^2 × 3^2 (2 × 2 × 3 × 3)
- Sum of divisors
- 91
- Sum of proper divisors
- 55
- Prime?
- No
- Perfect square?
- Yes (√36 = 6)
- Classification
- Abundant
Prime factorization, step by step
- 1Startn = 36
- 2Divide by smallest prime 236 ÷ 2 … running quotient
- 3Divide by smallest prime 2intermediate ÷ 2 … running quotient
- 4Divide by smallest prime 3intermediate ÷ 3 … running quotient
- 5Divide by smallest prime 3intermediate ÷ 3 … running quotient = 1 — done
- 6Collect the factors36 = 2 × 2 × 3 × 3 = 2^2 × 3^2
- 7Build every divisorMultiply combinations of the prime factors → 9 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factor pairs
36 is a perfect square — √36 = 6 appears once in the middle pair.
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Formula
n = p₁^a₁ × p₂^a₂ × … ; divisor count = (a₁+1)(a₂+1)…
Pro tips
- • The divisor count comes straight from the prime exponents: 36 = 2²·3² has (2+1)(2+1) = 9 divisors.
- • A perfect square always has an odd number of divisors because the middle factor pairs with itself.
- • Perfect numbers equal the sum of their proper divisors (6 = 1+2+3); the next ones are 28 and 496.
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