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What is the largest 3 digit number to have an odd number of factors?

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What is the largest 3 digit number to have an odd number of factors? [#permalink]

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Re: What is the largest 3 digit number to have an odd number of factors? [#permalink]

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New post 09 Mar 2016, 20:38
It is basically asking what is the biggest 3 digit square number. Answer is 'E'

Tip- All squares have odd numbers of factors.
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Re: What is the largest 3 digit number to have an odd number of factors? [#permalink]

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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


Some info on ODD/EVEN number of FACTORS..
1) ODD FACTORS-
a) if there are odd factors of an integer, that integer will be a square..
b) If the integer has 3 factors only, it is square of a PRIME number..

2) EVEN FACTORS-
a) If an integer has even number of factors, it will not be a Square..
b) If an integer has 2 factors, its a PRIME number

Here we are looking for largest 3-digit number, which has odd factors..

so this number must be square and since it asks for the largest 3-digit number..
We can look for the largest number given-961 , which is 31^2..

Also we know 900=30^2 so answer has to be equal to or greater than 30..
check for 31^2..

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Re: What is the largest 3 digit number to have an odd number of factors? [#permalink]

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New post 09 Mar 2016, 21:51
All squares have odd number of factors.
Highest square 31^2 =961
Answer E
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Re: What is the largest 3 digit number to have an odd number of factors? [#permalink]

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New post 14 Mar 2016, 05:36
Remember whenever the question says odd number odd number of factors we must conclude that its a perfect square.
Hence E is correct which is a perfect square of 31
hence E
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Re: What is the largest 3 digit number to have an odd number of factors? [#permalink]

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New post 05 Jan 2018, 10:08
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


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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Re: What is the largest 3 digit number to have an odd number of factors?   [#permalink] 05 Jan 2018, 10:08
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