O guia abaixo ainda não está disponível em português e é apresentado em inglês. A calculadora está totalmente traduzida.
Como usar esta calculadora
- Enter a whole number of 2 or more.
- The factorization appears instantly in exponent form and expanded form.
- The divisor count and list are shown for numbers up to 10¹².
Fórmula
Every integer greater than 1 can be written uniquely as a product of primes (the fundamental theorem of arithmetic). The calculator uses trial division: divide by 2 and 3, then by numbers of the form 6k ± 1 up to the square root of what remains. The number of divisors is the product of (exponent + 1) over all prime factors.
n = p₁^a₁ × p₂^a₂ × … × pₖ^aₖ
Number of divisors = (a₁ + 1)(a₂ + 1)…(aₖ + 1)
Example
- 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, ÷ 5 = 1.
- 360 = 2³ × 3² × 5.
- Number of divisors = (3+1)(2+1)(1+1) = 24.
Perguntas frequentes
Is 1 a prime number?
No. A prime has exactly two distinct divisors, 1 and itself. The number 1 has only one divisor.
What is a factor tree?
A diagram that splits a number into two factors repeatedly until only primes remain. The leaves of the tree are the prime factorization.
Why use prime factorization?
It's the basis for finding the GCF and LCM, simplifying fractions and radicals, and many cryptography algorithms.