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What is the greatest prime factor of 8^12 - 2^30?

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Carcass
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What is the greatest prime factor of 8^12 - 2^30? [#permalink] New post   24 Jun 2021, 09:40
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What is the greatest prime factor of 8^12 - 2^30?

A. 2
B. 3
C. 5
D. 7
E. 11
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D
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Re: What is the greatest prime factor of 8^12 - 2^30? [#permalink] New post   24 Jun 2021, 09:43
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Carcass wrote:
What is the greatest prime factor of 8^12 - 2^30?

A. 2
B. 3
C. 5
D. 7
E. 11


To determine the greatest prime factor of 8^12 - 2^30, we must find the prime factorization of 8^12 - 2^30

Given: 8^12 - 2^30
Rewrite 8 as 2³ to get: (2³)^12 - 2^30
Apply Power of Power rule to get: 2^36 - 2^30
Factor out 2^30 to get: 2^30(2^6 - 1)
Evaluate: 2^30(64- 1)
Simplify: 2^30(63)
Factor 63 to get: (2^30)(3)(3)(7)

At this point, we can see that the greatest prime factor is 7

Answer: D
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Re: What is the greatest prime factor of 8^12 - 2^30? [#permalink]
24 Jun 2021, 09:43
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