(4 ^17)-(2^28)=(2^34)-(2^28)=2^28(2^6-1)=2^28*63=2^28*7*9
since largest prime number in 2^28*7*9 is 7 so answer is d
Greatest prime factor
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abhishekg21
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Good question - and like many exponent questions this one comes down to:
1) Finding common bases
2) Factoring common terms to turn addition/subtraction into multiplication
First, we need to get a common base of 2:
2^34 - 2^28
Then we can factor out the 2^28 term:
2^28 (2^6 - 1)
Now we know that the greatest prime factor of 2^28 is 2 (2 is its only PRIME factor), so we're left with 2^6 - 1, which is:
64-1 = 63
63 = 9*7 = 3*3*7
7 is the greatest prime factor, so the answer is D.
1) Finding common bases
2) Factoring common terms to turn addition/subtraction into multiplication
First, we need to get a common base of 2:
2^34 - 2^28
Then we can factor out the 2^28 term:
2^28 (2^6 - 1)
Now we know that the greatest prime factor of 2^28 is 2 (2 is its only PRIME factor), so we're left with 2^6 - 1, which is:
64-1 = 63
63 = 9*7 = 3*3*7
7 is the greatest prime factor, so the answer is D.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
