Divisibility criteria

$$432$$

It ends with a even number, so it is divisible by $2$.

The sum of its digits is $9$, so it is divisible by $3$ and $9$.

It is divisible by $2$ and $3$, so it also has to be divisible by $6$.

$$1188$$

It ends with an even number, so it is divisible by $2$.

The sum of its digits is $18$, which is a multiple of $3$ and $9$, so it is divisible by $3$ and $9$.

It is divisible by $2$ and $3$, so it also has to be divisible by $6$.

Its last two digits are a multiple of $4$, so it is divisible by $4$.

The difference of the sum of its even and odd numbers is $0$, so it is divisible by $11$.

$$217$$

The difference of its first two digits with the double of the units is $7$, so it is divisible by $7$.

$$250$$

It ends in zero, so it is divisible by $2$, by $4$, by $5$ and by $10$.

Its last two digits are a multiple of $25$, so it is divisible by $25$.

Its last three digits are a multiple of $125$, so it is divisible by $125$.

$$330$$

It finishes in zero, so it is divisible by $2$, by $5$ and by $10$.

The sum of its digits is a multiple of $3$, so it is divisible by $3$.

It is divisible by $2$ and $3$, so also it has to be divisible by $6$.

The difference of the sum of its even and odd numbers is $0$, so it is divisible by $11$.