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If r, s and t are consecutive integers, what is the greatest prime fac

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If r, s and t are consecutive integers, what is the greatest prime fac  [#permalink]

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New post 07 Mar 2017, 10:54
1
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A
B
C
D
E

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Re: If r, s and t are consecutive integers, what is the greatest prime fac  [#permalink]

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New post 07 Mar 2017, 11:09
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Let R = x, S = x+1, T = x+2

3^r + 3^s + 3^t = 3^x + 3^(x+1) + 3^(x+2) = 3^x(1+3+9) = 3^x *13

Therefore greatest prime factor of 3^r + 3^s + 3^t is 13

Answer is E) 13
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Re: If r, s and t are consecutive integers, what is the greatest prime fac  [#permalink]

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New post 07 Mar 2017, 12:42
Let’s pick smart numbers.

Let r =0, let s= 1 and let t= 2

Hence the equation becomes 3^0+ 3^1 + 3 ^2

Which is equal to 1+3+9

= 13 = 13*1

Therefore the greatest prime factor is 13. Hence E.
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Re: If r, s and t are consecutive integers, what is the greatest prime fac  [#permalink]

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New post 09 Mar 2017, 13:48
As they are consequative we can write it so: 3^r(1+3^1+3^2)=3^r*13
So answer is 13 (E)
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Re: If r, s and t are consecutive integers, what is the greatest prime fac  [#permalink]

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New post 15 Mar 2017, 15:40
Bunuel wrote:
If r, s and t are consecutive integers, what is the greatest prime factor of 3^r + 3^s + 3^t ?

A) 3
B) 5
C) 7
D) 11
E) 13


Let’s say r = 1, s = 2, and t = 3; then we have:

3^1 + 3^2 + 3^3 = 3^1(1 + 3 + 9) = 3(13)

Let’s say r = 2, s = 3, and t = 4; then we have:

3^2 + 3^3 + 3^4 = 3^2(1 + 3 + 9) = 3^2(13)

We see that regardless of the 3 consecutive positive integers we select, the largest prime will always be 13 since the other factor is always a power of 3.

Answer: E
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Re: If r, s and t are consecutive integers, what is the greatest prime fac  [#permalink]

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Re: If r, s and t are consecutive integers, what is the greatest prime fac   [#permalink] 09 Feb 2019, 11:10
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