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If x = 2^74 - 2^70, what is the largest prime factor of x?

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Bunuel
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If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   30 Aug 2018, 00:17
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If \(x = 2^{74} - 2^{70}\), what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11
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C
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Re: If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   30 Aug 2018, 00:32
2^74-2^70
= 2^70(2^4-1)
= 2^70 (16-1)
= 2^70*3*5

Hence, the largest prime factor is 5.

So, the correct answer is option (C).
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Re: If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   30 Aug 2018, 01:13
x = 2^74 - 2^70
x = 2^70 ( 2^4 - 2^0)
x = 2^70 (16 - 1)
x = 2^70 * 15
x = 2^70 * 3^1 * 5^1
The largest prime factor is 5.
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If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   30 Aug 2018, 01:47
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Bunuel wrote:
If \(x = 2^{74} - 2^{70}\), what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11


Given, \(x = 2^{74} - 2^{70}\)
Factor out the common term \(2^{70}\),
\(x=2^{70}(2^4-1)=2^{70}*15\)
Prime factors are: 2,3,and 5
largest prime factor:5

Ans. (C)
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If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   30 Aug 2018, 06:41
Bunuel wrote:
If \(x = 2^{74} - 2^{70}\), what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11



\(x = 2^{74} - 2^{70}\)

= \(2^{70}(2^4 - 1)\)

= \(2^{70} * 15\)

= \(2^{70} * 3*5\)

So, 5 is the greatest prime factor.

The best answer is C.
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Re: If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   30 Aug 2018, 07:30
Bunuel wrote:
If \(x = 2^{74} - 2^{70}\), what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11

\(x = 2^{74} - 2^{70}\)

Or, \(x = 2^{70}(2^4 - 1)\)

Or, \(x = 2^{70}(15)\)

Or, \(x = 2^{70}(3*5)\), Thus the largest prime factor is 5, Answer must be (C)
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Re: If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   04 Sep 2018, 04:39
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Bunuel wrote:
If \(x = 2^{74} - 2^{70}\), what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11


We first factor 2^70 from both terms. Simplifying, we have:

2^70(2^4 - 1)

2^70 x 15

2^70 x 3 x 5

The largest prime factor is 5.

Answer: C
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Re: If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   23 Mar 2022, 09:15
Bunuel wrote:
If \(x = 2^{74} - 2^{70}\), what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11

\(x = 2^{74} - 2^{70}\)

Or, \(x = 2^{70}(2^{4} - 1)\)

Or, \(x = 2^{70}(16 - 1)\)

Or, \(x = 2^{70}*3*5\), So, Largest prime factor of x is 5, Answer must be (C)
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If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   23 Mar 2022, 09:18
Asked: If \(x = 2^{74} - 2^{70}\), what is the largest prime factor of x?

\(x = 2^{74} - 2^{70} = 2^{70}(2^4-1) = 2^{70}*(16-1) = 2^{70}*3*5\)

IMO C

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Re: If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink] New post   31 May 2023, 20:14
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Re: If x = 2^74 - 2^70, what is the largest prime factor of x? [#permalink]
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