Question

Fill in the blank. The smallest even number is __________.

Answer 1

Hint: Consider a few examples of even numbers. Compare them to find the smallest number from positive and negative integers. Thus find the smallest even number.

Complete step-by-step answer:
Now let us consider a few examples of even numbers, which when divided by 2 yield an integer with no remainder like 24, 32, 56 etc. But numbers like 3.7, 8.33 and 5.3 are not integers and they are not even.
Let us divide (+8) by 2, which will have no remainder, and the result will be (+4), which is an integer. If we are comparing 2 is smaller than 4 and 8. We may say that 2 is the smallest even number. But 0 is still smaller than 2.
If we are comparing between (-2) and (+2), we can say that 0 is the smallest. By defining the smallest further left to the number line, then 2 is still smaller than 4. But (-2) is smaller than 2. (-4) is still smaller than (-2). Thus going to the left of the number line there won’t be the smallest number as the negative numbers keep on going.
So, we can say that the smallest positive even number = 2.
The smallest even number = 0.
Thus the smallest even number is zero.

Note - We can use one of the most accepted definitions of even integer such that for an integer x, \[x=2k\], where k is also an integer. So \[x=\left| 2k \right|\], put k = 0, 1, 2……, we still would get the smallest even number as zero. If we are taking \[x=2k\], then it will further go down the side of the negative numbers. So take \[x=2k\].