Divide 14 into the sum of many natural numbers, and find the maximum value of the product of these numbers?

Question

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: ‘I am not aware of those numbers.’
Jacob: ‘I knew you wouldn’t be. I am not aware myself.’
John: ‘Now I know them!’
Jacob: ‘Now I know them, too!’

What are the two numbers?

Answer 1

3 + 3 + 3 + 3 + 2 = 14
3 * 3 * 3 * 3 * 2 = 162 is the maximum such product.