How to find the prime factorization
- Enter a whole number of 2 or more, up to 18 digits.
- Read its prime factorization with exponents, and the factors written out in full.
- See how many divisors it has and, for smaller counts, the full list.
Examples
| Number | Prime factorization | Divisors |
|---|---|---|
| 12 | 2² × 3 | 6 |
| 60 | 2² × 3 × 5 | 12 |
| 100 | 2² × 5² | 9 |
| 360 | 2³ × 3² × 5 | 24 |
| 97 | prime | 2 |
From factors to GCF and LCM
Line up the prime factorizations. The greatest common factor takes each shared prime with its smallest exponent; the least common multiple takes every prime with its largest exponent. For 60 = 2² × 3 × 5 and 72 = 2³ × 3², the GCF is 2² × 3 = 12 and the LCM is 2³ × 3² × 5 = 360.
Perfect squares and cubes
A number is a perfect square when every exponent in its factorization is even (36 = 2² × 3²) and a perfect cube when every exponent is a multiple of 3. The factorization also shows how to simplify a root: √72 = √(2³ × 3²) = 6√2.