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How many factors does the integer 9999 have?

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How many factors does the integer 9999 have? [#permalink] New post 22 Mar 2014, 01:26
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Difficulty:

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Question Stats:

56% (02:04) correct 44% (01:13) wrong based on 140 sessions
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15
[Reveal] Spoiler: OA

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Re: How many factors does the integer 9999 have? [#permalink] New post 22 Mar 2014, 03:43
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Mountain14 wrote:
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15


Finding the Number of Factors of an Integer

First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.

The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)

Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.

BACK TO THE ORIGINAL QUESTION:

\(9999 = 3^2*11*101\) --> the number of factors is (2+1)(1+1)(1+1)=12.

Answer: D.
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Re: How many factors does the integer 9999 have? [#permalink] New post 26 Apr 2014, 10:16
+1 for D :lol: , concept mentioned in GMATClub QUANT BOOK....do read to brushup basic and advance quant topics :idea:
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Re: How many factors does the integer 9999 have? [#permalink] New post 26 Nov 2014, 02:53
9999 = 3^2 * 11 * 101
and hence 2*2*3 = 12 distinct factors
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How many factors does the integer 9999 have? [#permalink] New post 24 Feb 2015, 12:58
We start with the prime factorization, as shown in the illustration.

Then, to find the number of factors, we add one to each of the powers and multply these additions.

So,

(2+1)*(1+1)*(1+1)
3*2*2
12

So, there are 12 factors in total.
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Re: How many factors does the integer 9999 have? [#permalink] New post 28 Feb 2015, 07:04
Expert's post
Mountain14 wrote:
How many factors does the integer 9999 have?

A. 6
B. 8
C. 10
D. 12
E. 15


Factorise 9999 = 3 * 3 * 11 * 101
= 3^2 * 11^1 * 101^1
Number of factors = (2+1)(1+1)(1+1)
= 3*2*2
=12
Hence option D.

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Re: How many factors does the integer 9999 have? [#permalink] New post 01 Mar 2015, 08:18
So 9 has 3 factors.

9 appears 4 times in the number.

4(3) = 12.

I checked this method with a few different numbers, all consiting of repeated integers less than 10 and it worked.

88

8 has 4 factors therefore 88 has 4(2)= 8.

Can anyone confirm that this works?

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Re: How many factors does the integer 9999 have?   [#permalink] 01 Mar 2015, 08:18
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