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Even Number by definition any integer that can be divided exactly by 2.

To get an even number, multiply an integer by 2 or in mathematical statement it is 2n.

An even number (2x) is multiplied to any number (y) is 2x (y).

So, by associative principle of multiplication 2x(y) = 2 (x*y).

If (x*y) now represents any integer then 2(x*y)= 2n.

And 2n is an even number.

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Q: Is an even number times any number always even?
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Why is any number raised to a even power positive?

A positive number times a positive number is always positive. A negative number times a negative number is always positive. Therefore, any square number will be positive. Any number to the fourth power (a square times a square) will always be positive. And so on.


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Is even number times even number always even?

Yes, it is. Any whole number times an even number will be even. This is because whole numbers can be represented as the product of their prime factors. Every even number contains 2 as a prime factor (thereby excluding all even numbers above 2 from being prime.) Additionally, the product of any two numbers is equal to the product of their prime factors. This means that the result of multiplying an even number by a whole number will always have a prime factor of 2, making it an even number.


Why is the product of two odd numbers odd?

Let me show this to you by an example : Suppose we wish to multiply 3 and 7. Product or Multiplication by any device is actually carried by the process of addition of 3 seven times, i.e. 3+3+3+3+3+3+3 = 21. Because the two numbers are odd, the result is always odd. To Summarize, addition of an odd number(i.e. 3) to itself an odd number of times(i.e. 7) always results in an odd number. The product of an even and an odd number always results in an even number because addition of even number any number of times is always even and an odd number added to itself an even number of times also results in an even number. For ex. 7*2 = 14, here 7(odd number) is added 2(even number) times, i.e. 7+7=14 which is even.


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Why is the sum os an even and odd number a odd number?

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When you multiply any number of even numbers will the product always be odd?

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