Prime Factorization Calculator
Enter a whole number to break it into prime factors.
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Prime factorization
Prime factorization
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Is it prime?
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Number of divisors
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Sum of all divisors
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Prime Factorization Calculator by TheCalcTools
How the Prime Factorization Calculator works
Every whole number above 1 is either prime or a product of primes in exactly one way (the fundamental theorem of arithmetic). The calculator divides by 2, by 3 and then by numbers of the form 6k ± 1 up to the square root.
From the exponents you get the divisor count: if n = p^a × q^b × …, it has (a + 1)(b + 1)… divisors.
The formula
n = p₁^a₁ × p₂^a₂ × …; number of divisors = (a₁ + 1)(a₂ + 1)…
Worked example
Using the default values shown in the calculator:
| Whole number (2 or more) | 360 |
|---|
- 360 = 2³ × 3² × 5.
- It has 24 divisors, which add up to 1,170.
Result:
| Prime factorization | 2³ × 3² × 5 |
|---|---|
| Is it prime? | No, it is composite |
| Number of divisors | 24 |
| Sum of all divisors | 1,170 |
Frequently asked questions
What is the prime factorization of 360?
2³ × 3² × 5. It has (3+1)(2+1)(1+1) = 24 divisors.
Is 1 a prime number?
No. Primes have exactly two divisors, and 1 has only one.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.