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

Question

What is the greatest prime factor of 8^12 - 2^30? 
 
A. 2
B. 3
C. 5
D. 7
E. 11

Skywalker18 · Accepted Answer

8^12 - 2^30
=(2^3)^12 - 2^30
= 2^36 - 2^30
= 2^30 (2^6 -1)
= 2^30 * (64-1)
= 2^30 * 63
= 2^30 * 9 *7 
= 2^30 * 3^2 * 7
greatest prime factor is 7
Answer D

BrentGMATPrepNow · Answer

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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HKD1710 · Answer

8^12 - 2^30?

8 = 2^3
8^12 = 2^36

2^36 - 2^30 = 2^30 (2^6 - 1) = 2^30 (64 - 1) = 2^30 (63) = 2^30 (7*3*3)

hence 2,3,7 are the prime factors of 8^12 - 2^30. here, 7 is the greatest prime factor.

Option D is correct.

AkshdeepS · Answer

My take:

8  ^{12}  -  2^{30}

2  ^{3*12}   - 2  ^{30}

2^{36}   - 2^{30}

2^{30} (2^6-1)

2^{30} * 63

2^{30}*3*3*7

Hence "7" is the GREATEST prime (D)

Nunuboy1994 · Answer

In order to solve this question we need to factor out the set of exponents until we find a prime number.

8^12-2^30 
4^24-2^30
(2^24)( 2^12)-2^30
2^36-2^30
2^30-(2^6-1) 
2^30-(64-1)
2^30-(63)

prime factorization of 63

(3)(3)(7)

Seven is the largest prime number and thus the answer

JeffTargetTestPrep · Answer

We can simplify the given expression:

(2^3)^12 - 2^30

2^36 - 2^30

2^30(2^6 - 1) = 2^30(63) = 2^30 x 9 x 7 = 2^30 x 3^2 x 7

So the largest prime factor is 7.

Answer: D

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

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

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