A new December and a new bunch of puzzles from mscroggs.co.uk.

14 is even, so 2 is a factor. The other factor is 7, a prime, so it can’t be constructed by multiplying lower numbers.

100 d100: One factor is 2, to get an even product the lowest possible way. Then the other factor of the product is a prime p, in this case 101, to make the product impossible. (Anything lower could be reached with 1⁹⁸ * 2 * p.) The product is 202.