Prime Factorization Calculator
Enter a positive integer to get its prime factorization, plus the divisor count, divisor sum, full list of divisors, and a primality check.
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Input
Enter a positive integer to see its prime factorization and divisor information at a glance.
Enter a whole number of 1 or more (up to one trillion).
Result
Prime factorization
360 = 2^3 × 3^2 × 5
Number of divisors
24
Sum of divisors
1,170
Is prime
No
Divisors (24)
1
2
3
4
5
6
8
9
10
12
15
18
20
24
30
36
40
45
60
72
90
120
180
360
How it works
- Trial division checks each prime starting from 2, dividing as many times as possible to find the exponent of each prime factor, then writes the result as 2^a x 3^b and so on.
- The number of divisors equals the product of each exponent plus one, and the sum of divisors is the product of the geometric series for each prime factor.
- A number is reported as prime when it is greater than 1 and has exactly one prime factor with exponent 1.
- The number 1 has no prime factors, so its only divisor is 1 and its divisor count is 1.
Frequently asked questions
- How is the prime factorization computed?
- By trial division: it tests primes starting from 2, counts each prime's exponent, and writes the result as 2^a × 3^b …. For example, 360 becomes 2³ × 3² × 5.
- How are the divisor count and divisor sum found?
- The divisor count is the product of each exponent plus one, and the divisor sum is the product of each prime's geometric series. For 360 (2³×3²×5) the divisor count is 4 × 3 × 2 = 24.
- What happens if I enter 1 or a prime number?
- The number 1 has no prime factors, so its only divisor is 1 (count of 1). A number greater than 1 is judged prime when it has exactly one prime factor with an exponent of 1.
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