What is the largest 3 digit. . . .

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

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

Vincen wrote: ↑

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?

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