When the dividend is not 0 (for example, 3÷0), because "any number multiplied by 0 is equal to 0, but it cannot be equal to a number that is not 0 (for example, 3)", the quotient of the division formula does not exist at this time-that is, 0 times of any number cannot be non-zero.

When the dividend is 0, that is, the division formula is 0÷0, because "any number multiplied by 0 equals 0", the quotient can be any number-that is, 0 times of any number equals 0.

Meaning of 0:

0 is an integer from-1 to 1, even number, smallest natural number and rational number. 0 is neither positive nor negative, but the dividing point between positive and negative numbers.

0 has no reciprocal, the reciprocal of 0 is 0, the absolute value of 0 is 0, the square of 0 is 0, the square root of 0 is 0, the cube root of 0 is also 0, 0 times any number equals 0, and the power of 0 of any number except 0 equals 1.

0 cannot appear as a denominator or divisor in a fraction. All multiples of 0 are 0, and 0 divided by any non-zero real number equals 0.