Bunuel wrote:
ebliss wrote:
Can someone please explain how we can go from 2^4 * 2^96 - 2^96 to 2^96 (16-1) ?
Thanks!
Sure.
What is the greatest prime factor of 2^100 - 2^96?A. 2
B. 3
C. 5
D. 7
E. 11
\(2^{100} - 2^{96}=2^4*2^{96}-2^{96}\).
Now, factor out 2^{96}: \(2^4*2^{96}-2^{96}=2^{96}(2^4-1)=2^{96}*15=2^{96}*3*5\). The greatest prime factor is 5.
Answer: C.
Hope it's clear.
@bunuel..2^96-2^96=2^1 according to index laws..in our factorised equation 2^4*2^96-2^96 the answer is 16*2=32..can we do prime factorisation on 32 where by k/2 +k/3 +k/5--->32/2+32/3+32/5?would we just take the 5 as our largest factor?but we know 5 is not a factor of 32..where am i missing the details please tell me..thanks in advance
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