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Re: What is the greatest prime factor of 2^10*5^4 – 2^13*5^2 + 2^14?
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20 Dec 2014, 07:58

1

JusTLucK04 wrote:

What is the greatest prime factor of 2^10*5^4 – 2^13*5^2 + 2^14? (A) 2 (B) 3 (C) 7 (D) 11 (E) 13

Easy One..

First take 2^10 as common, as shown below - 2^10(5^4 - 2^3*5^2 + 2^4) 2^10(625 - 200 6) 2^10 * 441 Find factors of 441 ie 21 * 21 The greatest prime factor is 7.

Re: What is the greatest prime factor of 2^10*5^4 – 2^13*5^2 + 2^14?
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25 Oct 2015, 09:16

time consuming, but definitely not a 700-level question. we can factor 2^10 first, and we remain with 5^2(5^2 - 2^3)+2^4

25-8 = 17, so we have 25*17 + 16, which is 441. I did not start doing the prime factorization, since it is more time consuming than trying to divide by each option choice. it is definitely not divisible by 11, so D is out. Divide by 13, well, 13*3 = 39, and we are left with 51, which is not divisible by 13, E out. Try by 7, works, so definitely the GCF is 7.