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Suppose that \(b\)  is a positive integer greater than or equal to 2. When 197 is converted to base \(b\) , the resulting representation has 4 digits. What is the number of possible values for b?

tertre  Mar 15, 2017

Best Answer 

 #1
avatar+19653 
+10

Suppose that is a positive integer greater than or equal to 2. 

When 197 is converted to base b, the resulting representation has 4 digits.

What is the number of possible values for b?

 

\(\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}\)

 

b is 4 or 5

 

laugh

heureka  Mar 15, 2017
 #1
avatar+19653 
+10
Best Answer

Suppose that is a positive integer greater than or equal to 2. 

When 197 is converted to base b, the resulting representation has 4 digits.

What is the number of possible values for b?

 

\(\begin{array}{|rcll|} \hline 197_{10} &=& 11000101_2 \\ 197_{10} &=& 21022_3 \\ 197_{10} &=& 3011_{\color{red}4} \\ 197_{10} &=& 1242_{\color{red}5} \\ 197_{10} &=& 525_6 \\ 197_{10} &=& 401_7 \\ 197_{10} &=& 305_8 \\ 197_{10} &=& 238_9 \\ 197_{10} &=& 197_{10} \\ \cdots \\ \hline \end{array}\)

 

b is 4 or 5

 

laugh

heureka  Mar 15, 2017

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