Prime Number

What is the last digit \textit{d} of the 9-digit number 19700019\textit{d}, given that the number is prime?
Source: NCTM Mathematics Teacher, November 2006

SOLUTION
The last digit \textit{d} could be 1,3,7, or 9.
\textit{d} cannot be 3 because 197000193\div 3=65666731.
\textit{d} cannot be 9 because 197000199\div 9=21888911.
197000197=197000000+197
=197(10^6+1)
\textit{d} cannot be 7 because 197000197 is divisible by 197.
The last digit \textit{d} must be 1.

Answer: 1

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About mvtrinh

Retired high school math teacher.
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