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

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Intern
Joined: 26 Aug 2014
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How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

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04 Dec 2014, 01:32
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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
Senior Manager
Joined: 13 Jun 2013
Posts: 271
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

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04 Dec 2014, 01:43
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3
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)
Intern
Joined: 23 Jul 2013
Posts: 14
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 56306
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

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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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07 Jan 2017, 19:20
$$5^{17}+5^{20}=> 5^{17}(5^3+1) = 5^{17}*126=> 2*3^2*5^{17}*7$$
So it has 4 prime factors.
Hence D

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

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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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Joined: 04 Mar 2011
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Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

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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.

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Posts: 427
Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

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22 Aug 2018, 08:11
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

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

OA:D
$$5^{20} + 5^{17} = 5^{17}(5^3+1)=5^{17}(2*3^2*7)$$
Number of positive distinct prime factors$$=4 (2,3,5,7)$$
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Re: How many positive distinct prime factors does 5^20 + 5^17 have?  [#permalink]

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24 Aug 2018, 11:54
Four factors - 2,3,5 & 7. Take out 5^17 (5^3+1) ...do the prime factorization.
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Re: How many positive distinct prime factors does 5^20 + 5^17 have?   [#permalink] 24 Aug 2018, 11:54
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