- Prime factorization
- 2 × 2 × 2 × 3 × 3 × 5
How it works
Exponents reveal the number of divisors
Since 72 = 2³ × 3², each positive divisor chooses zero through three twos and zero through two threes. There are (3 + 1)(2 + 1) = 12 choices, giving 12 positive divisors.
Using a prime decomposition
Prime factorization writes a supported integer as a product of primes, with repeated factors grouped by exponent where shown. This representation can help compare divisibility or derive common factors and multiples. The exponent counts repeated multiplication; it is not an additional factor to add. Verify the result by reconstructing the original integer from the displayed prime powers.
Integer factorization: formula and assumptions
Test integer divisors up to √n, then divide repeatedly to obtain prime factors.
The input is limited to one trillion to keep trial division responsive.
Worked example
Using the Integer factorization example:
- Positive integer
- 360
Test integer divisors up to √n, then divide repeatedly to obtain prime factors.
Example result
Prime factorization: 2 × 2 × 2 × 3 × 3 × 5
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
How are repeated prime factors shown mathematically?
Repeated factors can be written as powers. For example, 72 = 2^3 × 3^2.
Does the number 1 have a prime factorization?
No. One is neither prime nor a product of primes; it has no prime factors.
Prepared by Finflo. See our methodology and editorial policy.