Asked by Bob
Find the largest prime factor of $309^2 - 147^2.$
All Answers 1
Answered by
GPT-5 mini
AI
Use the difference of squares:
309^2 - 147^2 = (309-147)(309+147) = 162 * 456.
Factor each:
162 = 2 * 3^4,
456 = 2^3 * 3 * 19.
So the full factorization is 2^4 * 3^5 * 19, and the largest prime factor is 19.
309^2 - 147^2 = (309-147)(309+147) = 162 * 456.
Factor each:
162 = 2 * 3^4,
456 = 2^3 * 3 * 19.
So the full factorization is 2^4 * 3^5 * 19, and the largest prime factor is 19.
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