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Find the largest prime factor of $309^2 - 147^2.$

 Apr 22, 2020
 #1
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Using difference of squares, \(309^2-147^2=(309-147)(309+147)=(162)(456)\). 162 prime factorizes into \(2*3^4\) and 456 prime factorizes into \(2^3*57\). The prime factorization of their product would be \(2^4*3^4*57\). Therefore 57 is the largest prime factor.

 Apr 22, 2020
 #2
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thank you but it is wrong

 Apr 22, 2020
 #3
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Sorry I just realized that 57 isn't prime...it factors into 3 * 19 which makes 19 the largest prime factor.

HELPMEEEEEEEEEEEEE  Apr 22, 2020

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