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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?

 Jan 20, 2020
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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.

 Jan 21, 2020

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