Hello all:
I ran into this problem on the GMATPrep test.
What is the greatest prime factor of 4^17 - 2^28?
A. 2
B. 3
C. 5
D. 7
E. 11
This was a tough one because had never dealt with adding and subtracting numbers w/exponents before. I converted 4^17 to 2^34 and I was stumped from there. My natural instinct had me choose A. However, the OA is D. I tried to work through the problem to see exactly why it is D.
By quickly analyizing the patterns of the powers of 2, I could see that every 4th power of 2 ends in the units digit of 6 (ie, 2^4 =16, 2^8 = 256), and every 2nd power of ends in a units digit of 4 (ie, 2^2 = 4, 2^6 = 64). Therefore I assumed that 2^34 (4^17) would end in the units digit of 4, and 2^28 would end in the units digit of 6, the difference of which would have a units digit of 8.
That is as far as I got and I could only eliminate 5 from the answers.
Could anyone help me out with this?
I ran into this problem on the GMATPrep test.
What is the greatest prime factor of 4^17 - 2^28?
A. 2
B. 3
C. 5
D. 7
E. 11
This was a tough one because had never dealt with adding and subtracting numbers w/exponents before. I converted 4^17 to 2^34 and I was stumped from there. My natural instinct had me choose A. However, the OA is D. I tried to work through the problem to see exactly why it is D.
By quickly analyizing the patterns of the powers of 2, I could see that every 4th power of 2 ends in the units digit of 6 (ie, 2^4 =16, 2^8 = 256), and every 2nd power of ends in a units digit of 4 (ie, 2^2 = 4, 2^6 = 64). Therefore I assumed that 2^34 (4^17) would end in the units digit of 4, and 2^28 would end in the units digit of 6, the difference of which would have a units digit of 8.
That is as far as I got and I could only eliminate 5 from the answers.
Could anyone help me out with this?
