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A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are 4, A, and 7.  If the integer is a multiple of 17_10, what is the units digit?

 Jul 25, 2019
 #1
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4A70 [Hex Number]
3210=[16^3 * 4] + [16^2 * 10] + [16^1 * 7] + [16^0 * 0]
         =   16,384    +   2560        +     112         +      0
         =19056 mod 16 = 16 - Since the remainder is 1 < 17, it therefore follows that the first digit is 1. So, the Hex number would be:4A71 =19,056 + 1 =19,057 mod 17 in base 10 = 0.

 Jul 25, 2019
 #2
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Hex   4 A 7 ?  divisible by 17

 

4 x 16^3 +

10 x 16^2 +

7 x 16 = 19056       19056/17 = 1120.94117      1121x 17= 19057

 

Untis digit needs to be 1

 

4 x 16^3 +

10 x 16^2 +

7x 16 +

1               =  19057    which is divisible by 17

 Jul 25, 2019

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