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

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Math Expert
Joined: 02 Sep 2009
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If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

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29 Aug 2018, 23:17
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73% (00:46) correct 27% (00:55) wrong based on 117 sessions

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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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Re: If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

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29 Aug 2018, 23:32
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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Joined: 19 Apr 2018
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Re: If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

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30 Aug 2018, 00:13
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]

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30 Aug 2018, 00:47
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]

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30 Aug 2018, 05:41
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]

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30 Aug 2018, 06:30
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]

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04 Sep 2018, 03:39
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.

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Re: If x = 2^74 - 2^70, what is the largest prime factor of x?   [#permalink] 04 Sep 2018, 03:39
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# If x = 2^74 - 2^70, what is the largest prime factor of x?

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