Identify Multiples and Factors 3 - Reasoning

The statement that the product of an even number and any integer is an even number, and therefore a multiple of 2, is indeed true. Multiplication and division principles confirm this fact. When an even number is multiplied by any other integer, whether it's odd or even, the result is always an even number. This is because even numbers can be defined as multiples of 2, meaning they can be expressed as 2n, where n is an integer. Multiplying this by any other integer, say m, gives us 2n × m, which is also a multiple of 2, thus ensuring the product remains even.

For example, taking the even number 8 and multiplying it by the odd number 3 results in 24, which is an even number and a multiple of 2. Similarly, multiplying the even number 12 by the odd number 5 yields 60, which again is an even number and a multiple of 2. These examples illustrate the rule and prove the truth of the statement. Therefore, whenever you multiply an even number by an odd number, you can be assured that the product will indeed be a multiple of 2, confirming the statement as true.