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# If n=2^4*3*5, how many factors of n are greater than or equal to 8 and

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Math Expert
Joined: 02 Sep 2009
Posts: 54434
If n=2^4*3*5, how many factors of n are greater than or equal to 8 and  [#permalink]

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09 Aug 2017, 01:33
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Difficulty:

45% (medium)

Question Stats:

67% (02:23) correct 33% (02:11) wrong based on 87 sessions

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If $$n=2^4*3*5$$, how many factors of n are greater than or equal to 8 and less than or equal to 30?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 15

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If n=2^4*3*5, how many factors of n are greater than or equal to 8 and  [#permalink]

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09 Aug 2017, 01:50
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Bunuel wrote:
If $$n=2^4*3*5$$, how many factors of n are greater than or equal to 8 and less than or equal to 30?

(A) 8
(B) 9
(C) 10
(D) 12
(E) 15

Total number of factors of $$n = 5*2*2 = 20$$
No of factors less than 8 are {1,2,3,4,5,6} = 6
No of factors greater than 30 are {$$2^4*3$$, $$2^3*5$$, $$2^4*5$$, $$3*5*2^2$$, $$3*5*2^3$$, $$3*5*2^4$$} = 6

Hence total number of factors between 8 & 30 (both inclusive) = 20-6-6 = 8

Option A
If n=2^4*3*5, how many factors of n are greater than or equal to 8 and   [#permalink] 09 Aug 2017, 01:50
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# If n=2^4*3*5, how many factors of n are greater than or equal to 8 and

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