Prime Factorization Calculator
Break a number into its prime factors, in exponent form and as a factor tree, and see whether it is prime.
Change the values and press Calculate to work out your own figures.
Enter a whole number to write it as a product of primes.
360
├── 2
└──┐
180
├── 2
└──┐
90
├── 2
└──┐
45
├── 3
└──┐
15
├── 3
└──┐
5Show the working
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
How to use it
Enter a whole number to write it as a product of primes.
The answer is exact: whole numbers of any size up to 30 digits are handled without rounding, and Show the working lists every step.
Key facts
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
How it works
Divide by the smallest prime that goes in exactly (2, then 3, then 5 and so on), write it down, and repeat with what is left until you reach 1. Every whole number above 1 has exactly one prime factorization.
Questions
Is 1 a prime number?
No. A prime has exactly two factors, 1 and itself; 1 has only one.
What is the prime factorization of 100?
2 × 2 × 5 × 5, or 2² × 5².
Formulas
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
Sources
Limitations
- Numbers have at most 30 digits; factor lists and prime factorizations are limited to 10¹².