481,618 views
40 votes
40 votes
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
by
2.7k points

1 Answer

11 votes
11 votes

Answer: 9990

========================================================

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.

------------------------

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
by
2.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.