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How many positive distinct prime factors does 5^20 + 5^17 have?

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How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

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How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five
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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

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New post 04 Dec 2014, 01:43
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pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five


\(5^{20} + 5^{17}\) = \(5^{17}(5^3+1)\)

=\(5^{17}(125+1)\)
=\(5^{17} (126)\)
=\(5^{17} .2.7.3^2\)
thus total number of distinct prime factors are 4 (2,3,5,7)
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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

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New post 31 Jan 2016, 18:59
manpreetsingh86 wrote:
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five


\(5^{20} + 5^{17}\) = \(5^{17}(5^3+1)\)

=\(5^{17}(125+1)\)
=\(5^{17} (126)\)
=\(5^{17} .2.7.3^2\)
thus total number of distinct prime factors are 4 (2,3,5,7)



Hi,

Shouldn't it be 1, 2, 3, 5 and 7? Please confirm. Thanks.
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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

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New post 31 Jan 2016, 22:17
Meetup wrote:
manpreetsingh86 wrote:
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five


\(5^{20} + 5^{17}\) = \(5^{17}(5^3+1)\)

=\(5^{17}(125+1)\)
=\(5^{17} (126)\)
=\(5^{17} .2.7.3^2\)
thus total number of distinct prime factors are 4 (2,3,5,7)



Hi,

Shouldn't it be 1, 2, 3, 5 and 7? Please confirm. Thanks.


1 is NOT a prime number.

Check here for more: math-number-theory-88376.html

Hope it helps.
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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

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New post 07 Jan 2017, 19:20
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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

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New post 09 Feb 2018, 03:29
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five


5^20 + 5^ 17

take 5^17 common on both sides of the sign = 5^17( 5^3 + 1) = 5^17( 125+1) = 5^17 (126)

14 x 9 = 126 so prime are 2,3,7
5^17 prime is 5

prime factors are 5, 2, 3, 7

1 is not prime
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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

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New post 12 Feb 2018, 17:32
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five


We can simplify the given expression by first factoring 5^17 as a common factor:

5^17(5^3 + 1)

5^17(126)

5^17 x 2 x 63

5^17 x 2 x 3^2 x 7

Thus, 5^20 + 5^17 has 4 distinct prime factors.

Answer: D
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Re: How many positive distinct prime factors does 5^20 + 5^17 have?   [#permalink] 12 Feb 2018, 17:32
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How many positive distinct prime factors does 5^20 + 5^17 have?

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