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

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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]
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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]
$$5^{17}+5^{20}=> 5^{17}(5^3+1) = 5^{17}*126=> 2*3^2*5^{17}*7$$
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]
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]
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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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]
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]
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]
why will we do +1? is it any property?
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Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]
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