GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Jul 2020, 19:08

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The number 10010 has how many positive integer factors?

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 24 Jul 2017
Posts: 11
Location: India
Schools: Copenhagen (A)
GMAT 1: 630 Q42 V34
GPA: 2.8
The number 10010 has how many positive integer factors?  [#permalink]

### Show Tags

Updated on: 11 Feb 2018, 00:04
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:52) correct 23% (01:57) wrong based on 58 sessions

### HideShow timer Statistics

The number 10010 has how many positive integer factors?

A. 30
B. 32
C. 34
D. 36
E. 38

Originally posted by sxsd on 10 Feb 2018, 23:59.
Last edited by Bunuel on 11 Feb 2018, 00:04, edited 1 time in total.
Renamed the topic.
Math Expert
Joined: 02 Sep 2009
Posts: 64951
Re: The number 10010 has how many positive integer factors?  [#permalink]

### Show Tags

11 Feb 2018, 00:06
sxsd wrote:
The number 10010 has how many positive integer factors?

A. 30
B. 32
C. 34
D. 36
E. 38

Factorize: 10010 = 2*5*7*11*13.

Number of factors = (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 32.

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.
_________________
Re: The number 10010 has how many positive integer factors?   [#permalink] 11 Feb 2018, 00:06