Kata

You have to code a function getAllPrimeFactors, which takes an integer as parameter and returns an array containing its prime decomposition by ascending factors. If a factor appears multiple times in the decomposition, it should appear as many times in the array.

exemple: getAllPrimeFactors(100) returns [2,2,5,5] in this order.

This decomposition may not be the most practical.

You should also write getUniquePrimeFactorsWithCount, a function which will return an array containing two arrays: one with prime numbers appearing in the decomposition and the other containing their respective power.

exemple: getUniquePrimeFactorsWithCount(100) returns [[2,5],[2,2]]

You should also write getUniquePrimeFactorsWithProducts, which returns an array containing the prime factors to their respective powers.

exemple: getUniquePrimeFactorsWithProducts(100) returns [4,25]

Errors, if:

• n is not a number
• n not an integer
• n is negative or 0

The three functions should respectively return [], [[],[]] and [].

Edge cases:

• if n=0, the function should respectively return [], [[],[]] and [].
• if n=1, the function should respectively return [1], [[1],[1]], [1].
• if n=2, the function should respectively return [2], [[2],[1]], [2].

The result for n=2 is normal. The result for n=1 is arbitrary and has been chosen to return a usefull result. The result for n=0 is also arbitrary but can not be chosen to be both usefull and intuitive. ([[0],[0]] would be meaningfull but wont work for general use of decomposition, [[0],[1]] would work but is not intuitive.)