Bunuel 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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