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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]  22 Mar 2014, 01:26
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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]  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.

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Re: How many factors does the integer 9999 have? [#permalink]  26 Apr 2014, 10:16
+1 for D , concept mentioned in GMATClub QUANT BOOK....do read to brushup basic and advance quant topics
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Re: How many factors does the integer 9999 have? [#permalink]  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]  24 Feb 2015, 12:58

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.
Attachments

factorization.png [ 1.65 KiB | Viewed 986 times ]

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Re: How many factors does the integer 9999 have? [#permalink]  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]  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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