What is the greatest prime factor of ((2^4 )^2)−1?
(A) 3
(B) 5
(C) 11
(D) 17
(E) 19
(2^4 )^2−1 = (16)^2 −1 = 256 −1 = 255. Since the question asks for the greatest prime factor, we eliminate 19,the greatest number. Now, we start with the next largest number and work our way up the list; the first number that divides into 255 evenly will be the answer. Dividing 17 into 255 gives
17)255 = 15
Hence, 17 is the largest prime factor of (2^4 )^2
−1. The answer is (D).
(A) 3
(B) 5
(C) 11
(D) 17
(E) 19
(2^4 )^2−1 = (16)^2 −1 = 256 −1 = 255. Since the question asks for the greatest prime factor, we eliminate 19,the greatest number. Now, we start with the next largest number and work our way up the list; the first number that divides into 255 evenly will be the answer. Dividing 17 into 255 gives
17)255 = 15
Hence, 17 is the largest prime factor of (2^4 )^2
−1. The answer is (D).
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