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 \(n\) =
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How to Use this Prime Decomposition Calculator

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

\[12 = 2^2 \cdot 3\]

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