What is the greatest prime factor of:
4 (to the 17th power) minus 2 (to the 28th power). This is a GMAT question that I'm having trouble with. Please give a step by step explanation. Thanks
2006-10-06 05:27:06 · 7 answers · asked by Jason A 1 in Science & Mathematics ➔ Mathematics
4^17-2^28
= (2^2)^17 = 2^28( 4= 2^2)
= 2^34-2^28((x^a)^b= x^(ab)
= 2^28(2^6-1) (factoring 2^28 common)
highest prime factor is 2^6-1 or 63 is 7
so ans is 7
2006-10-06 05:36:19 · answer #1 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
4^17 - 2^28 ==
4^17 - 4^14 ==
(4^3 * 4^14) - 4^14 =
63 * 4^14
prime factors of 4^14 are: 2
prime factors of 63 are 3 and 7
prime factors overal are 2 3 7
7 is greatest prime factor
2006-10-06 05:34:35 · answer #2 · answered by Gypsy Doctor 4 · 1⤊ 0⤋
4^17 = (2^2)^17 = 2^34.
Therefore, we get
2^34 - 2^28 = 2^28 * (2^6 - 1) = 2^28 * 63.
The greatest prime factor of 63 is 7. (The only other prime factor is 3.)
2006-10-06 10:41:34 · answer #3 · answered by dutch_prof 4 · 0⤊ 0⤋
dividing throughout by 4
the equation becomes
1^17-1/4^28
1-(1/4)^28
multiplying by 4
4-1x1^27=
Now check the answers and write the one that come close eliminating anything below 3and above 4. This is how we answer gmat where we by process of elimination in some question like this we reach the answers fast.
2006-10-06 06:38:17 · answer #4 · answered by Mathew C 5 · 0⤊ 0⤋
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2016-12-04 08:20:22 · answer #5 · answered by deparvine 4 · 0⤊ 0⤋
4^17 - 2^28 = 2^34 - 2^28
= (2^6)(2^28) - 2^28
= (2^6 - 1)(2^28)
= (64 - 1)(2^28)
= (63)(2^28)
= (3^2)(7)(2^28)
The largest factor is 7.
2006-10-06 05:47:28 · answer #6 · answered by Anonymous · 0⤊ 0⤋
deleted
2006-10-06 05:34:47 · answer #7 · answered by Joe C 3 · 0⤊ 0⤋