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- Breaks any whole number up to 1 trillion into its prime factors.
- Writes the answer with exponents, such as 360 = 2³ × 3² × 5.
- Tells you if the number is prime.
- Lists the number of divisors, their sum and all divisors.
How to use the prime factorization calculator
Enter a whole number
Any whole number from 2 up to 1,000,000,000,000.
Read the factorization
See it in exponent form and expanded form.
Check the extras
See whether it is prime, its divisors and the division steps.
What is prime factorization?
Prime factorization means writing a number as a product of prime numbers. Every whole number greater than 1 has exactly one prime factorization (the fundamental theorem of arithmetic). The calculator divides by 2, then 3, 5, 7 and so on until only 1 is left.
Divisor formulas
If n = p^a × q^b × r^c, then
Number of divisors = (a + 1)(b + 1)(c + 1)
Sum of divisors = (1 + p + … + p^a)(1 + q + … + q^b)(1 + r + … + r^c)
Example 1: 360
Divide by primes until you reach 1.
- Prime factorization 2³ × 3² × 5
- Number of divisors (3 + 1)(2 + 1)(1 + 1) = 24
- Sum of divisors 1,170
Example 2: more numbers
Quick results.
- 97 Prime
- 1,024 2¹⁰ (11 divisors)
- 600,851,475,143 71 × 839 × 1,471 × 6,857
- 1,000,000,007 Prime
Where prime factorization helps
GCF and LCM
Find the greatest common factor and least common multiple.
Simplifying fractions
Cancel shared prime factors from top and bottom.
Simplifying square roots
Pull out pairs of primes from under the root.
Math contests
Count divisors fast with the exponent formula.
Simplify fractions with the fraction calculator, simplify roots with the square root calculator, or work with huge numbers in the big number calculator.
Prime factorization calculator FAQ
What is the prime factorization of 360?
360 = 2³ × 3² × 5, or 2 × 2 × 2 × 3 × 3 × 5.
Is 1 a prime number?
No. A prime has exactly two divisors, 1 and itself, so 1 is not prime and has no prime factorization.
How do you find prime factors?
Divide the number by the smallest prime that goes into it, then repeat with the result until you reach 1.
How many divisors does a number have?
Add 1 to each exponent in its prime factorization and multiply. 360 has (3+1)(2+1)(1+1) = 24 divisors.
What is the largest number I can enter?
Up to 1,000,000,000,000 (one trillion).
Is 97 a prime number?
Yes. 97 has no divisors other than 1 and 97.