One Tree per Number

Two trees for 72. One starts with $8\cdot 9$. The other starts with $6\cdot 12$. Both end with the same primes: $2\cdot 2\cdot 2\cdot 3\cdot 3$.

This always happens. Every whole number above 1 has exactly one prime factorization. Only the order of the primes can change.

So a missing prime can be found. In $2\cdot 5\cdot n = 70$, the primes you have make 10. 70 divided by 10 is 7, so n is 7.