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Look at the multiples of 5.

5, 10, 15, 20, 25, 30, 35, 40, 45, 50,

We see that the one’s digits are alternately 5 and 0, and no other digit ever appears in this list.

So, we get our test of divisibility by 5.

If the ones digit of a number is 0 or 5, then it is divisible by 5.

Let us explain this rule. Any number ... cba can be written as:

... + 100c + 10b + a

Since 10, 100 are divisible by 10 so are 10b, 100c, ... which in turn, are divisible by 5 because 10 = 2 × 5. As far as number a is concerned it must be divisible by 5 if the number is divisible by 5. So a has to be either 0 or 5.