Factor Calculator

Ricerca dei Fattori

Trova ogni divisore intero, le proprietà matematiche e l'elenco dei divisori per qualsiasi intero positivo.

How Does a Factor Calculator Work?

A factor calculator finds all positive integers that divide a given number with zero remainder. The algorithm tests every integer from 1 to the square root of the input number. Each successful division produces a factor pair — the divisor and the quotient. Testing up to the square root is sufficient because factors always come in pairs where one is ≤ √n and the other is ≥ √n.

The factor calculator above processes numbers up to 10,000,000. For each input, it returns the complete factor list, factor pairs, prime factorization, divisibility chart, and number classification (prime, composite, perfect, abundant, or deficient). All calculations run locally in your browser using trial division.

Factor Rainbow Visualization

Factor Pair Arcs

12471428

Factor Calculator Worked Examples

28

6 factors · Perfect number

1, 2, 4, 7, 14, 28

28 is a perfect number because the sum of its proper factors (1 + 2 + 4 + 7 + 14 = 28) equals 28 itself. 28 = 2² × 7, giving (2+1)(1+1) = 6 factors.

42

8 factors · Abundant

1, 2, 3, 6, 7, 14, 21, 42

72

12 factors · Abundant

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

144

15 factors · Perfect square

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

Frequently Asked Questions

Perfect squares always have an odd number of factors. The number 36 = 6² has 9 factors, and 144 = 12² has 15 factors. This happens because every factor pair contains 2 different numbers — except the square root, which pairs with itself. The factor count formula confirms this: for n = p₁^a₁ × p₂^a₂ × ..., the total factors = (a₁+1)(a₂+1)... All exponents in a perfect square are even, so each (aᵢ+1) is odd, and a product of odd numbers is odd.