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A palindrome is a number that is the same when read forwards and backwards, such as $43234$. What is the smallest five-digit palindrome that is divisible by $17$?

 Aug 15, 2023

Best Answer 

 #1
avatar+177 
+1

I wrote some computer code, and I found that 11611 is the smallest palindrome divisible by 17. 

 

In case you are curious, here is the code I wrote for this particular problem. Note I did not finish the code because I already found the smallest palindrome with the incomplete code.

 

int startNum = 10001;
int numToTest = startNum;
        for (int i = 0; i < 10; ++i){
            for (int j = 0; j < 10; ++j){
                if (numToTest % 17 == 0){
                    System.out.println(numToTest + " is divisible by 17");
                }
                else{
                    System.out.println(numToTest + " is not divisible by 17");
                }
                numToTest = numToTest + 100;
            }
            startNum = startNum + 1010;
            numToTest = startNum;
        }

 Aug 16, 2023
 #1
avatar+177 
+1
Best Answer

I wrote some computer code, and I found that 11611 is the smallest palindrome divisible by 17. 

 

In case you are curious, here is the code I wrote for this particular problem. Note I did not finish the code because I already found the smallest palindrome with the incomplete code.

 

int startNum = 10001;
int numToTest = startNum;
        for (int i = 0; i < 10; ++i){
            for (int j = 0; j < 10; ++j){
                if (numToTest % 17 == 0){
                    System.out.println(numToTest + " is divisible by 17");
                }
                else{
                    System.out.println(numToTest + " is not divisible by 17");
                }
                numToTest = numToTest + 100;
            }
            startNum = startNum + 1010;
            numToTest = startNum;
        }

The3Mathketeers Aug 16, 2023
 #2
avatar+121 
0

To find the smallest five-digit palindrome that is divisible by 17, we can start by considering the multiples of 17 until we find a palindrome.

First, we need to find the smallest multiple of 17 that is a five-digit number. To do this, we can divide 10000 (the smallest five-digit number) by 17:

\[10000 \div 17 \approx 588.23.\]

So, the smallest multiple of 17 that is a five-digit number is \(17 \times 588 = 9996\).

Next, let's check the next multiples of 17 to find a palindrome:

\[17 \times 589 = 9993\]
\[17 \times 590 = 10030\]
\[17 \times 591 = 10047\]

The next multiple, \(17 \times 592\), is a five-digit number and is equal to \(99944\). This is a palindrome, so the smallest five-digit palindrome that is divisible by 17 is \(99944\).

 Aug 16, 2023

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