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What is the largest positive integer with only even digits that is less than 10,000 and is a multiple of 9?

 May 18, 2020
edited by Guest  May 18, 2020
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The largest integer less than 10000 is 8888, since each digit is the largest even.

8 * 4= 32, which isn't divisible by 9.

 

All multiples of 9 equal or less than 32:

 

 

9

18

27

 

We can't get 9 or 27 since those are odd and we can only subtract two(to get the next largest even)

 

So 32 - 18 = 14, so we have14/2 = 7. So we can only subtract 8/2 = 4 sets of 2's from the ones digit, so that's 8880.7-4 is 3 so we subtract 3*2 = 6 from the tens so 8820.

 

8+8+2 = 18

 

If you don't understand anythign feel free to ask!

 May 18, 2020

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