Which of the following properties states that changing the order of the factors does not change their product?

The property that states changing the order of the factors does not affect their product is the Commutative Property of Multiplication. This means that if you have two numbers, say (a) and (b), you can multiply them in either order and the result will be the same: (a \times b = b \times a).

Understanding this property is essential because it allows flexibility in computation and problem-solving. For instance, when simplifying expressions or solving equations, you can rearrange terms to make calculations easier without worrying about changing the outcome.

The Associative Property, while related to multiplication, deals with how factors are grouped in multiplication (e.g., ((a \times b) \times c = a \times (b \times c))), but it does not address the order of the factors. The Distributive Property involves distributing a multiplication over addition or subtraction (e.g., (a(b + c) = ab + ac)) and is not concerned with the order of factors in multiplication. Lastly, the Inverse Property refers to the concept of balancing an operation with its opposite (e.g., multiplying by a reciprocal for multiplication) and does not pertain to the order of factors.