There are many calculators online that will deliver factorizations instantaneously. You won't understand the process, but it's a shortcut.
No.
295 = 5 × 59
no
yes but some shortcuts are too risky
3 x 5 = 15
280 140,2 70,2,2 35,2,2,2 7,5,2,2,2
There aren't any.
If a person doesn't know the proper method to solve a problem or any shortcuts, brute force is the only method he can use, which might help him make an educated guess.
You can eliminate the fractions before proceeding to solve the equation to allow for easy factorization.
The prime factorization of 212 is 2 x 2 x 53. 16 is not a factor of 212.
2 x 2 x 5 x 11
I think you mean that the prime factorization is 2 times 3 times 5. To solve, just perform the multiplication: 2x3x5=30