NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 20:46 It is currently 25 Apr 2024, 20:46
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

What is the total number of positive factors of 6400?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619045 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
What is the total number of positive factors of 6400? [#permalink] New post   23 Jun 2020, 09:40
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

79% (00:56) correct 21% (02:02) wrong based on 84 sessions
Hide Show timer Statistics
What is the total number of positive factors of 6400?

A. 24
B. 27
C. 54
D. 68
E. 72

Show Spoiler
What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 54 (4) 68
ShowHide Answer
Official Answer
B
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [1]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: What is the total number of positive factors of 6400? [#permalink] New post   23 Jun 2020, 09:47
1
Kudos
Factors of 6400 = 2*2*2*2*2*2*2*2*5*5
=> 2^8*5^2

The number of factors = (8+1)(2+1) = 9*3 = 27

IMO B

Posted from my mobile device
avatar
B
dhawalsachdeva
Intern
Intern
Joined: 30 May 2019
Posts: 24
Own Kudos [?]: 12 [0]
Given Kudos: 188
Send PM
Re: What is the total number of positive factors of 6400? [#permalink] New post   23 Jun 2020, 09:52
Factors of 6400 are - 2^8 * 5^2

Total numbers of factors is given by - (Power of 1st prime factor +1) * (Power of 2nd prime factor +1) * and so on

Therefore, Answer = (8+1)*(2+1) =27

That is choice B.

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: What is the total number of positive factors of 6400? [#permalink] New post   23 Jun 2020, 10:07
1
Kudos
Expert Reply
Bunuel wrote:
What is the total number of positive factors of 6400?

A. 24
B. 27
C. 54
D. 68
E. 72

Show Spoiler
What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 54 (4) 68


CONCEPT: If \(N = a^p*b^q*c^r...\)
where a, b, c... are distinct primes
Number of factors of \(N = (p+1)*(q+1)*(r+1)*...\)


\(6400 = 64*100 = 2*8*5^2\)

Factors of 6400 = (8+1)*(2+1) = 27

Answer: Option B
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5344
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: What is the total number of positive factors of 6400? [#permalink] New post   23 Jun 2020, 11:26
Bunuel wrote:
What is the total number of positive factors of 6400?

A. 24
B. 27
C. 54
D. 68
E. 72

Show Spoiler
What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 54 (4) 68


Asked: What is the total number of positive factors of 6400?

\(6400 = 2^8*5^2\)
The total number of positive factors of 6400 = 9*3 = 27

IMO B
User avatar
S
dimri10
Manager
Manager
Joined: 16 May 2011
Posts: 240
Own Kudos [?]: 308 [0]
Given Kudos: 64
Concentration: Finance, Real Estate
GMAT Date: 12-27-2011
WE:Law (Law)
Send PM
GMAT ToolKit User
What is the total number of positive factors of 6400? [#permalink] New post   23 Jun 2020, 13:30
6400 is a perfect square (80*80), so just looking at the answers, the only odd number is 27.
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22055 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: What is the total number of positive factors of 6400? [#permalink] New post   27 Jun 2020, 05:59
Expert Reply
Bunuel wrote:
What is the total number of positive factors of 6400?

A. 24
B. 27
C. 54
D. 68
E. 72

Show Spoiler
What is the total number of different divisors including 1 and the number that can divide the number 6400?
(1) 24 (2) 27 (3) 54 (4) 68


Solution:

Getting 6400 into prime factors, we have:

6400 = 64 x 100 = 2^8 x 5^2

Thus, 6400 has (8+1)(2+1) = 9 x 3 = 27.

Answer: B
GMAT Club Bot
gmatclubot
Re: What is the total number of positive factors of 6400? [#permalink]
27 Jun 2020, 05:59
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions