Very last digit of 4
If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer?
Details and assumptions
The last digit of an integer is the right most digit. As an explicit example, the last digit of is 3.
The answer is 5.
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10 solutions
Moderator note:
This solution merely shows that there are at least 5 possibilities. It gives a sufficient condition, but not a necessary condition.
It needs to explain why "all multiples of 4 end with the following digits only". When you notice a pattern, you should seek to explain it fully.
Moderator note:
This solution merely shows that there are at most 5 possibilities. It gives a necessary condition, which may not be sufficient.
For example, if we consider multiples of 10, we can apply the same argument:
When a positive integer is multiplied by 10 , so the new number must be an even positive integer, hence the last digit may be 0, 2, 4,6, or 8.
However, we know that the last digit must be 0, so there is only 1 possibility.
If we give a look at the multiplication table of 4 it appears as :
4 * 1 = 4
4 * 2 = 8
4 * 3 = 12
4 * 4 = 16
4 * 5 = 20
4 * 6 = 24 and so on........
We will notice that all multiples of 4 end with the following digits only :
0, 2, 4, 6, 8
"Thus there are only 5 possible Distinct Digits"