What is the largest 3 digit number to have an odd number of factors?
A. 625
B. 729
C. 841
D. 943
E. 961
The OA is E.
I got confused here. What does "odd number of factors" mean?
What is the largest 3 digit. . . .
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
IMPORTANT CONCEPT: All positive integers have a EVEN number of positive factors EXCEPT integers that are squares of integersVincen wrote:What is the largest 3 digit number to have an odd number of factors?
A. 625
B. 729
C. 841
D. 943
E. 961
Squares of integers (e.g., 1, 4, 9, 16, 25, 36, etc) have an ODD number of positive factors.
So, the question is really asking us "What is the largest 3 digit number that is the SQUARE OF AN INTEGER?"
Let's find out.
30² = 900, so 900 will have an odd number of positive factors
31² = 961, so 961 will have an odd number of positive factors
32² = 1024, so 1024 will have an odd number of positive factors.
Of course 1024 is a FOUR-DIGIT number.
So, 961 must be the greatest 3-digit number with an ODD number of positive factors.
Answer: E
Cheers,
Brent
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7222
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
A number greater than 1 will have an odd number of factors only if it's a perfect square. The largest 3-digit perfect square is 31 x 31 = 961 (since 32 x 32 = 1,024).Vincen wrote:What is the largest 3 digit number to have an odd number of factors?
A. 625
B. 729
C. 841
D. 943
E. 961
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7222
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Since perfect squares have an odd number of factors, we need to determine the largest 3-digit perfect square. Thus, the answer is 961 since 31 x 31 = 961.
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews