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What is the greatest prime factor of 2^{34} - 2^{28}?

 Dec 24, 2019

Best Answer 

 #1
avatar+333 
+2

Factor out the expression.

\(2^{28}(2^{6}-1)\)

\(2^{28}(64-1)\)

\(2^{28}*63\)

 

Since all the factors of \(2^{28}\) are 2's, for now, the smallest prime factor is 2.

Next factor out 63 into \(3^{2}*7\)

The prime factors in this expression are 2,3, and 7 now.

7, being the largest, is the greatest prime factor of this expression.

 Dec 24, 2019
 #1
avatar+333 
+2
Best Answer

Factor out the expression.

\(2^{28}(2^{6}-1)\)

\(2^{28}(64-1)\)

\(2^{28}*63\)

 

Since all the factors of \(2^{28}\) are 2's, for now, the smallest prime factor is 2.

Next factor out 63 into \(3^{2}*7\)

The prime factors in this expression are 2,3, and 7 now.

7, being the largest, is the greatest prime factor of this expression.

hellospeedmind Dec 24, 2019

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