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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5
If the sum of the digits is divisible by three, that means that the number is divisible by 3. If the number ends in 0, that means the number is divisible 10,2, and 5. Since the number is divisible by 2 and 3, it is also divisible by 6.
Therefore, the number is ALWAYS divisible by 10,2,5,3, and 6.
That is 5 numbers.
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0
Answer:
4
Step-by-step explanation:
Since the integer ends in 0, it is divisible by 2 and 5. Because the sum of its digits is divisible by 3, the number is divisible by 3, and we know that a number divisible by both 2 and 3 is also divisible by 6. If the number is 30, however, then it is not divisible by 4, 8, or 9. So exactly 4 of the numbers in the original problem statement must divide it.
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