Why do not all multiples of four end in four?

Answer 1

Quite simply, there is no rule that states that all multiples of a one-digit number have to end with that same digit, and no reason why it should be so. In the case of 2, and simply because 10 is a multiple of 2, the last digit (of a multiple of 2) is also a multiple of 2 - but it doesn't even have to be 2; it can be 0, 2, 4, 6, 8. Similar with 5, since 10 is also a multiple of 5.

In the case of 4, since 100 is a multiple of 4, the last two digits of any multiple of 4 are a multiple of 4. For instance, take the number 4524 - since the last two digits (24) are a multiple of 4, the whole number is.

Suggestion: Take some multiples of 4 (or of some other number), and try to look for patterns.

Note that for some numbers, the patterns are so complicated, that it's easier to figure out whether a number is a multiple of another by actually doing the division.