Prime Factorization Calculator
Break any whole number from 2 up to one trillion into its prime factors. The result is shown in exponent form and written out in full, along with whether the number is prime and how many divisors it has.
- Written out
- 2 × 2 × 2 × 3 × 3 × 5
- Is it prime?
- No
- Number of divisors
- 24
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Formula
How to use it
- Enter a whole number between 2 and 1,000,000,000,000.
- Read the prime factorization in exponent form.
- Check the divisor count or the prime test if you need them.
Worked examples
Prime factors of 360
- Prime factorization
- 2³ × 3² × 5
- Written out
- 2 × 2 × 2 × 3 × 3 × 5
- Is it prime?
- No
- Number of divisors
- 24
Prime factors of 1,001
- Prime factorization
- 7 × 11 × 13
- Is it prime?
- No
- Number of divisors
- 8
Checking 97
- Prime factorization
- 97
- Is it prime?
- Yes
- Number of divisors
- 2
How it is worked out
Divide by 2 for as long as it goes evenly, then by 3, then by each odd number in turn, stopping once the divisor squared is bigger than what is left. Whatever remains above 1 is itself prime.
For 360: 360 ÷ 2 = 180, ÷ 2 = 90, ÷ 2 = 45, ÷ 3 = 15, ÷ 3 = 5, and 5 is prime. So 360 = 2³ × 3² × 5, and it has (3 + 1) × (2 + 1) × (1 + 1) = 24 divisors.
Facts about primes
A prime has exactly two divisors, 1 and itself. The number 1 is neither prime nor composite, and 2 is the only even prime. The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
To test whether a number is prime you only need to try divisors up to its square root — for anything under one trillion, that is at most one million.
Questions people ask
What is the prime factorization of 360?
2³ × 3² × 5, or 2 × 2 × 2 × 3 × 3 × 5.
What is the prime factorization of 100?
2² × 5², or 2 × 2 × 5 × 5.
Is 97 a prime number?
Yes. It is not divisible by 2, 3, 5 or 7, and the next prime, 11, is already larger than its square root.
Is 1 a prime number?
No. A prime must have exactly two distinct divisors, and 1 has only one.