how could we know that a theorem is suitable for proof by induction?

Question

Theorems like (factorization theorem) aren't suitable to be proven with induction since induction requires that the property tackled with our set of variables must be satisfied consecutively; (prime numbers aren't consecutive). So, how could we be sure that any theorem that we want to prove by induction, would be suitable for that? Is the answer: If it was proven as a false theorem by induction?