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?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
4
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?
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