Prove that the product of any even number and any integer is always even

The product of any even number and any integer is always even is proved

Solution:

Proof that any integer multiplied by 2 is even comes from the simple fact that every even number has 2 as a factor, the product of an even number with any even or odd number, will also have 2 as a factor, and thus also be even.

Any even number can be expressed as ,

where k>= 1 and let ‘a’ be any integer.

Then the result of any even number multiplied by any integer is

which is divisible by 2 yielding no remainder, and hence by definition an even number.

Hence any integer multiplied by an even number will always be an even number.

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step-by-step explanation: