Answer:
14, 2 and -8 all can be divided by the greatest number, 2.
Explanation:
If you do not want a decimal number for each, then first you would choose an even number. Odd numbers will likely make 14, 2 and -8 a decimal.
Dividing by 1 makes the numbers 14, 2 and -8. 1 is an odd number, but it does not affect any of the numbers. However, there may be a better number.
Dividing by 2 makes the numbers 7, 1 and -4. So far this number works to divide them all.
Dividing by 4 makes the numbers 3.5, 0.5 and -2. Only one number is not a decimal, so this does not work.
Dividing by 6 makes the numbers 2.333..., 0.333... and -1.333... All of these numbers are decimals. This will not work either.
We can conclude that any number greater than 2 will not make all the numbers whole. They will be made irrational and decimal.
So 2 is the greatest number that can divide into all of the numbers.