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?

BIGChungus Jul 25, 2019

#1**+2 **

**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.**

Guest Jul 25, 2019

#2**+3 **

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

ElectricPavlov Jul 25, 2019