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# How many values can natural number n take, if n! is a multiple of 7^6

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Manager
Joined: 03 Mar 2018
Posts: 182
How many values can natural number n take, if n! is a multiple of 7^6  [#permalink]

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10 Apr 2018, 12:14
4
00:00

Difficulty:

55% (hard)

Question Stats:

42% (01:41) correct 58% (01:22) wrong based on 36 sessions

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How many values can natural number n take, if n! is a multiple of $$7^6$$ but not $$7^9$$?

(A) 7
(B) 21
(C) 14
(D) 12
(E) 20

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Manager
Joined: 05 Feb 2016
Posts: 141
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: How many values can natural number n take, if n! is a multiple of 7^6  [#permalink]

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10 Apr 2018, 12:33
1
itisSheldon wrote:
How many values can natural number n take, if n! is a multiple of $$7^6$$ but not $$7^9$$?

(A) 7
(B) 21
(C) 14
(D) 12
(E) 20

41! contains $$7^5$$ as factor
42! contains $$7^6$$ as factor
55! contains $$7^8$$ as factor
56! contains $$7^9$$ as factor

So total n=55-42+1=14

option C
Re: How many values can natural number n take, if n! is a multiple of 7^6 &nbs [#permalink] 10 Apr 2018, 12:33
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