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What is the largest 3 digit. . . .

This topic has 2 expert replies and 1 member reply

What is the largest 3 digit. . . .

Post Tue Oct 03, 2017 4:51 pm
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?

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Post Mon Oct 09, 2017 4:22 pm
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
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).

Answer: E

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Scott Woodbury-Stewart Founder and CEO

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Post Tue Oct 03, 2017 6:22 pm
Thanks Brent. I didn't know that. Now I understand the question and your answer.

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GMAT/MBA Expert

Post Tue Oct 03, 2017 4:59 pm
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
IMPORTANT CONCEPT: All positive integers have a EVEN number of positive factors EXCEPT integers that are squares of integers
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

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Brent Hanneson – Founder of GMATPrepNow.com
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