What is the largest prime factor of the expression 3^8 − 2^12?

Question

A. 2
B. 3
C. 5
D. 17
E. 29

KSBGC · Accepted Answer

Given

3^8 − 2^{12}

= (3^4)^2 - (2^6)^2

= ( 3^4 + 2^6) (3^4 - 2^6)

= (81 + 64) (81 - 64)

= (145 ) ( 9^2 - 8^2)

= (5 * 29) ( 9 + 8) ( 9- 8)

= 5 * 29 * 17 * 1

The best answer is E.

Manick9 · Answer

If you see it, it is in the (a+b)(a-b) which is = (3^4+2^6)(3^4-2^6) = (81+64)(81-64) = (145)(17)
Therefore, highest prime factor is 17.

Bismarck · Answer

OA:E
 3^8 − 2^{12} =(3^4)^2 − (2^6)^2 =(3^4-2^6)(3^4+2^6)=(3^2-2^3)(3^2+2^3)(3^4+2^6)=(9-8)(9+8)(81+64)=1*17*145=1*17*5*29

KSBGC · Answer

u can further break down 145

145 = 29 * 5

Hope it's clear.

Manick9 · Answer

That's right. I missed the last option.

ScottTargetTestPrep · Answer

We see that the expression 3^8 - 2^12 is a difference of squares. Thus, we have:

3^8 - 2^12 = (3^4 + 2^6)(3^4 - 2^6) = (3^4 + 2^6)(3^2 + 2^3)(3^2 - 2^3)

3^4 + 2^6 = 81 + 64 = 145 = 5 x 29

3^2 + 2^3 = 9 + 8 = 17

3^2 - 2^3 = 9 - 8 = 1

So 3^8 - 2^12 = 5 x 29 x 17, and the largest prime factor is 29.

Answer: E

Kinshook · Answer

Asked: What is the largest prime factor of the expression 3^8 − 2^12?

3^8 − 2^12 = 9ˆ4 - 8ˆ4 = (9ˆ2 - 8ˆ2)(9ˆ2 + 8ˆ2) =

= (9-8)(9+8)(9ˆ2+8ˆ2) = 1*17*145 = 17*5*29

The largest prime factor of the expression {3^8 − 2^12} = 29

IMO E

Oppenheimer1945 · Answer

3^8-2^12=(3^4+2^6)(3^4-2^6)=17*(81+64)=17*145=17*5*29

bumpbot · Answer

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What is the largest prime factor of the expression 3^8 − 2^12?

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What is the largest prime factor of the expression 3^8 − 2^12?

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