Question

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

Answer 1

Any even number will always have a factor of 2. Therefore, you will essentially be multiplying the integer by 2.

Answer 2

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
`2^k` ,

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

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

`2^k * a`

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.