How many factors does the integer 9999 have?

Question

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

Bunuel · Accepted Answer

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.

hangovrlyf · Answer

+1 for D

, concept mentioned in GMATClub QUANT BOOK....do read to brushup basic and advance quant topics :idea:

sanket1991 · Answer

9999 = 3^2 * 11 * 101
and hence 2*2*3 = 12 distinct factors

pacifist85 · Answer

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.

OptimusPrepJanielle · Answer

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. -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

ak1802 · Answer

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?

Posted from my mobile device

colorblind · Answer

Interesting.....but didnt work for 777.

GMATAcademy · Answer

I, for one, find it much easier to retain a formula if I understand it. Here's a video that goes over the logic behind the formula some of the responses are using:

https://www.youtube.com/watch?v=njePP0ZK2bY

Shiv2016 · Answer

9999 can also be written as (10000-1)

(10000-1)= ((10^4)- 1)= ((10^2)^2 - 1)

Applying (a^2-b^2)= (a+b) (a-b)

(10^2+1) (10^2-1)= 101*99= 101*3^2*11

Number of factors= (1+1)(2+1)(1+1)= 2*3*2= 12

AkshdeepS · Answer

9999 = 3 * 3 * 11 * 101

Add 1 to powers of all prime factors and multiply:

(2+1) (1+1) (1+1)

3*2*2

12

(D)

JeffTargetTestPrep · Answer

Breaking 9999 into primes we have:

9999 = 9 x 1111 = 9 x 101 x 11 = 3^2 x 101^1 x 11^1

So the total number of factors is (2 + 1)(1 + 1)(1 + 1) = 3 x 2 x 2 = 12.

Answer: D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

How many factors does the integer 9999 have?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

How many factors does the integer 9999 have?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards