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What is the largest 4- digit number that is divisible by 3, 6, and 9? Explain how you know.

What is the largest 4- digit number that is divisible by 3, 6, and 9? Explain how-example-1
User Vnshetty
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1 Answer

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Answer: 9990

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Step-by-step explanation:

Start with the largest four digit number possible (9999) and see if it's divisible by 3, 6 and 9

  • 9999/3 = 3333
  • 9999/6 = 1666.5
  • 9999/9 = 1111

When dividing the number over 6, we don't get a whole number. So 6 is not a factor of 9999, and we cross 9999 off the list.

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Decrease the number by 9. We do this because the result will be another multiple of 9 (which is automatically also a multiple of 3 as well, since 9 = 3*3)

So we go from 9999 to 9990

Repeat the last set of steps we did earlier

  • 9990/3 = 3330
  • 9990/6 = 1665
  • 9990/9 = 1110

Every result is a whole number, which shows that 9990 is a multiple of 3, 6 and 9. In other words, 9990 is divisible by 3, 6 and 9. It's the largest such 4 digit number.

User Hayward Oblad
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