If an integer ends in the digit $0$ and the sum of its digits is divisible by $3$, then how many of the numbers $2, 3, 4, 5, 6, 8, 9$ necessarily divide it?
Ok, so if it ends with a zero, that means it is divisible by ten. This means the number is divisible by both 5 and 2.
The sum of the digits is also divisible by 3, so that means it is divisible by 3.
Because it is divisible by 3 and 2, it is also divisible by 6.
6, 3, 5, 2, are the only ones that can necessarily divide it, so your answer is 4.