How many distinct integers are factors of 90? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 Feb 2017, 22:10

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# How many distinct integers are factors of 90?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Apr 2012
Posts: 276
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 5

Kudos [?]: 781 [0], given: 325

How many distinct integers are factors of 90? [#permalink]

### Show Tags

11 Feb 2013, 00:26
1
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:19) correct 23% (00:33) wrong based on 141 sessions

### HideShow timer Statistics

How many distinct integers are factors of 90?

A. 6
B. 8
C. 9
D. 10
E. 12

[Reveal] Spoiler:
Approach 2: Prime factorization:
21∗32∗51=90

Add 1 to each exponent and multiply them:
(1+1)(2+1)(1+1)=12

I did not follow the approach , why 're we adding 1 ? . I get confused with this type of problems . Where Can i find a clear explanation for this approach theoretically? Appreciate the help !

thanks
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Feb 2013, 00:41, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96457 [1] , given: 10751

Re: How many distinct integers are factors of 90? [#permalink]

### Show Tags

11 Feb 2013, 00:44
1
KUDOS
Expert's post
guerrero25 wrote:
How many distinct integers are factors of 90?

A. 6
B. 8
C. 9
D. 10
E. 12

[Reveal] Spoiler:
Approach 2: Prime factorization:
21∗32∗51=90

Add 1 to each exponent and multiply them:
(1+1)(2+1)(1+1)=12

I did not follow the approach , why 're we adding 1 ? . I get confused with this type of problems . Where Can i find a clear explanation for this approach theoretically? Appreciate the help !

thanks

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:

How many distinct integers are factors of 90?

A. 6
B. 8
C. 9
D. 10
E. 12

$$90=2*3^2*5$$, which means that the number of factors of 90 is: $$(1+1)(2+1)(1+1)=12$$.

Similar questions to practice:
how-many-odd-positive-divisors-does-540-have-106082.html
how-many-factors-does-36-2-have-126422.html
how-many-different-positive-integers-are-factor-of-130628.html
how-many-distinct-positive-factors-does-30-030-have-144326.html

Hope it helps.
_________________
Senior Manager
Joined: 10 Apr 2012
Posts: 276
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 5

Kudos [?]: 781 [0], given: 325

Re: How many distinct integers are factors of 90? [#permalink]

### Show Tags

12 Feb 2013, 02:59
Hope it helps.[/quote]

Hi Bunuel,Thanks you so Much .. After going through the other posts you mentioned here , I could do any problem related to factors now .
Intern
Joined: 16 May 2015
Posts: 46
Followers: 0

Kudos [?]: 9 [0], given: 11

How many distinct integers are factors of 90? [#permalink]

### Show Tags

27 Jul 2015, 02:41
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4365
Followers: 356

Kudos [?]: 3676 [0], given: 105

Re: How many distinct integers are factors of 90? [#permalink]

### Show Tags

27 Jul 2015, 03:07
katzzzz wrote:
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

The number of factors that you get is only the distinct factors and does not count the identical factors in case of perfect square twice..
eg 36=2^2*3^2..
no of factors= 3*3=9..
they are 1,2,3,4,6,9,12,18,36..
hope it clears the doubt
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

SVP
Joined: 08 Jul 2010
Posts: 1511
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 75

Kudos [?]: 1503 [0], given: 42

Re: How many distinct integers are factors of 90? [#permalink]

### Show Tags

27 Jul 2015, 03:40
katzzzz wrote:
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

Please refer two distinct concepts to calculate factors of any Number

1) By writing the Number as product of two Integers

2) By prime factorization and multiplying the powers of Distinct prime after adding one in each power of Primes
Attachments

File comment: www.GMATinsight.com

Factors.jpg [ 112.78 KiB | Viewed 3840 times ]

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html

Feel free to give a Kudos if it is a useful post .

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96457 [0], given: 10751

Re: How many distinct integers are factors of 90? [#permalink]

### Show Tags

27 Jul 2015, 03:57
katzzzz wrote:
Just want to clear a concept that the formula to compute the no of factors of a number includes identical factors?

2^ 1 ∗3^ 2 ∗5^ 1 =90

therefore, for perfect square, we need to eliminate the identical factors?

_________________
Intern
Joined: 16 May 2015
Posts: 46
Followers: 0

Kudos [?]: 9 [0], given: 11

How many distinct integers are factors of 90? [#permalink]

### Show Tags

27 Jul 2015, 07:22
Hi Chetan and GMAR Insight,
thanks. clear now.

Hi Bunnel,
I will search the topic first for my future posts. thanks.
How many distinct integers are factors of 90?   [#permalink] 27 Jul 2015, 07:22
Similar topics Replies Last post
Similar
Topics:
How many diferent positive integers are factors of 225 ? 2 26 Apr 2015, 19:23
16 How many factors does the integer 9999 have? 10 22 Mar 2014, 01:26
11 How many distinct positive factors does 30,030 have? 10 18 Dec 2012, 03:07
10 The positive integer 200 has how many factors? 11 17 Sep 2012, 05:24
19 How many different positive integers are factors of 441 9 13 Apr 2012, 01:42
Display posts from previous: Sort by