# Prime Decomposition

Instructions: Compute the prime decomposition of a non-negative integer value $$n$$. The value of $$n$$ needs to be integer and greater than or equal to 1

The integer $$n$$ =

More about Prime Decomposition: For an integer number $$n$$, there exists a unique prime decomposition, this is, a way of expressing this integer number $$n$$ as a product of different prime numbers (where those prime numbers can be repeated, or have multiplicity, as it is commonly said as well).

For example, the number $$n = 12$$ can be written as it follows

$12 = 3 \cdot 4$

Is this the prime decomposition of $$n = 12$$? Nope, because 3 is a prime number (it is divisible only by 1 and by itself), but 4 is not prime (because it is divisible by 2). So then, the decomposition shown above is a decomposition, but not the the prime decomposition. Now, observing that

$12 = 3 \cdot 4 = 3 \cdot 2 \cdot 2$

we can see that now $$n = 12$$ is decomposed as the product of primes only. Reordering the primes in ascending order, and grouping the primes with multiplicity, we get the neat expression

$12 = 2^2 \cdot 3$