Why is there no number which is divisible by zero?

Answer 1

There is no number which is divisible by zero because that would constitute a number that could have zero subtracted from it a specific number of times.

For instance; 12 is divisible by three, because three can be subtracted from 12 four times, giving a final result of zero.

Even if you subtract zero an infinite number of times, you cannot reach a quotient of zero from any number other than zero. Zero, however, is a special case. Zero divided by zero, even though it seems to meet the subtraction rule, does not constitute divisibility - it is an undefined.

In advanced mathematics, we do talk about infinity, and we do define that any number divided by zero is infinity, but we still by convention do not call any number ever divisible by zero.

Going further, the special case of zero divided by zero, while officially undefined, does have a definite value when you start talking about limits, but that is a topic for pre-calculus.