Factorize a number into coprime numbers I want to know if there is a way to factorize a number into coprime numbers; for example $N = a_1 \cdot a_2 \cdot a_3 \cdots a_i$ And $a_i$ and $a_j$ are coprime for any $i \ne j$ Thanks

You can construct this from the prime factorization. Just group all the appearances of the same prime factor to obtain $N=\prod p_i^{n_i}$. Since $p_i,p_j$ are distinct primes, any power of them has no non-unit common factors.