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Yes it is possible to determine if a product will be even or odd. To do this, we need to consider what an even number is. Even numbers are numbers with at least one factor of 2 (meaning they are divisible by 2). Thus, any product of numbers which contains at least one even number will result in an even product. If all of the numbers being multiplied together are odd, the product will be odd. If one or more of the numbers is even, the product will be even.
Any pair of one even and one odd number will have an even product and an odd sum.
The product of two odd numbers is always odd.
An even number can be divided by 2 evenly. An odd number will have a remainder of 1 when divided by 2. Odd times odd is always odd.
The product of two odd numbers is never even.