“the product of the factors” versus “the factors of the product”

Question

Could somebody please compare and contrast the meanings of the two phrases:

"the product of the factors"

and

"the factors of the product."

In terms of expressing possession. Thank you.

Answer 1

The factors go into the product's construction. Also, the product is the result of an operation on the factors.

The same can be said for a sum and its terms:

The terms go into the sum's construction. Also, the sum is the result of an operation on the terms.

Answer 2

The factors $a$, $b$, and $c$ have product $a\cdot b\cdot c$.

$a$, $b$, and $c$ are the factors of the product $abc$.

$abc$ is the product of the factors $a$, $b$, and $c$.

Answer 3

I think "the product of the factors" is a value with each factor in the exact expressing possession.And "the factors of the product." is a set of factor values, that means you can express these values in any order.