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All of the ID codes in Angelo’s school are three-digit positive integers. For Angelo’s ID code, the product of the digits is 216, the sum of the digits is 19, and the integer ID code is as large as possible. What is Angelo’s ID code?

 May 31, 2020
 #1
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Angelo's Code = 964

 May 31, 2020
 #2
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List the factors of 216.

 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216

 

Since his ID code is only three-digits, we can eliminate the numbers above 9, which leaves us to:

 - 1, 2, 3, 4, 6, 8, 9

 

Use these numbers to determine what 3 numbers add to equal 19 and multiply to equal 216.

 

The numbers in Angel's ID code include: 4, 6, and 9.

 

List the possible three-digit outcomes of 4, 6, 9 (hint - since there are three digits, there are 6 outcomes):

4-6-9

4-9-6

9-4-6

9-6-4

6-9-4

6-4-9

 

The last bit of information also tells us that the integer code is as large as possible. Picking from the list of possible three-digit outcomes, ask yourself, which is the largest possible?
 

Angelo's ID code is 9-6-4.

 

If you have any questions, don't be afraid to ask! I hope I explained well enough. 

:)

 May 31, 2020
edited by auxiarc  May 31, 2020

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