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Find the largest prime factor of 1,005,010,010,005,001. 

Can someone do this with algebra?

 Jun 10, 2024
 #1
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We have to make a really important observation to solve this problem. Note that

\(1,005,010,010,005,001 = \\ 1\times 10^{15} + 5 \times 10^{12} + 10\times 10^9 + 10\times 10^6 + 5 \times 10^3 + 1\times 10^0\\ \)

This value is equal to

\((10^3+1)^5\), which is equal to \(1001^5\)

 

Now, we have to find the largest prime factor of 1001. 

 

We know that \(1001=13*11*7\)

 

This means the largest prime factor is 13. 

 

Thanks! :)

 Jun 10, 2024

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