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Perfect square

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Motivatedtowin
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Perfect square [#permalink] New post   03 Dec 2014, 01:30
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The number theory states that :
A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
Could you please explain what this means :?:
If i have a number say: 4624.that will be 17*17*2*2*2*2
which is 2 factors of the odd number 17 :roll:
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EliLTG
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Re: Perfect square [#permalink] New post   03 Dec 2014, 07:56
Motivatedtowin wrote:
The number theory states that :
A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
Could you please explain what this means :?:
If i have a number say: 4624.that will be 17*17*2*2*2*2
which is 2 factors of the odd number 17 :roll:

Hi Motivated,

Interesting trivia! As a mathematician, I'm always interested to learn facts like that--but as a GMAT instructor, I always caution students about focusing too much on details like this that are extremely unlikely to appear on your exam!

As for your specific question, you are getting factors confused with prime factors. The rule you mentioned applies to the total list of factors of 4624, i.e. 1 * 4624, 2 * 2312, 4 * 1156...

Hope this helps!
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Motivatedtowin
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Re: Perfect square [#permalink] New post   03 Dec 2014, 09:35
EliLTG wrote:
Motivatedtowin wrote:
The number theory states that :
A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
Could you please explain what this means :?:
If i have a number say: 4624.that will be 17*17*2*2*2*2
which is 2 factors of the odd number 17 :roll:

Hi Motivated,

Interesting trivia! As a mathematician, I'm always interested to learn facts like that--but as a GMAT instructor, I always caution students about focusing too much on details like this that are extremely unlikely to appear on your exam!

As for your specific question, you are getting factors confused with prime factors. The rule you mentioned applies to the total list of factors of 4624, i.e. 1 * 4624, 2 * 2312, 4 * 1156...

Hope this helps!




Thank you so much ...The exam already has too much to study and work in itself :shock: But i just came across this and could not understand..So basically..say for a smaller number like 36:1*2*2*3*3, number of odd factors=3(ODD) and number of even factors equals 2(EVEN) :-D
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EliLTG
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Re: Perfect square [#permalink] New post   03 Dec 2014, 11:12
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Not quite!
The factors of 36 are:

1, 36
2, 18
3, 12
4, 9
6, 6

So, the odd factors are: 1, 3, and 9;
The even factors are 2, 4, 6, 12, 18, 36.
Does this help?
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KarishmaB
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Perfect square [#permalink] New post   Updated on: 17 Oct 2022, 01:21
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Motivatedtowin wrote:
The number theory states that :
A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
Could you please explain what this means :?:
If i have a number say: 4624.that will be 17*17*2*2*2*2
which is 2 factors of the odd number 17 :roll:



Here are a few interesting things about factors of perfect squares:

ONLY perfect squares will have odd number of total factors and ALL perfect squares will have an odd number of total factors.

A perfect square always has odd number of odd factors.

A perfect square always has even number of even factors.

The sum of all factors of a perfect square is always odd but if the sum of all factors of a number is odd, we cannot say that it must be a perfect square.

Originally posted by KarishmaB on 03 Dec 2014, 19:50.
Last edited by KarishmaB on 17 Oct 2022, 01:21, edited 1 time in total.
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Motivatedtowin
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Re: Perfect square [#permalink] New post   04 Dec 2014, 05:33
Thanks so much for the replies...Finally clarity :o
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Re: Perfect square [#permalink] New post   10 Sep 2022, 07:39
KarishmaB wrote:
Motivatedtowin wrote:
The number theory states that :
A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors.
Could you please explain what this means :?:
If i have a number say: 4624.that will be 17*17*2*2*2*2
which is 2 factors of the odd number 17 :roll:



Here are a few interesting things about factors of perfect squares:

ONLY perfect squares will have odd number of total factors and ALL perfect squares will have an odd number of total factors.

A perfect square always has odd number of odd factors.

A perfect square always has even number of even factors.

The sum of all factors of a perfect square is always odd but if the sum of all factors of a number is odd, we cannot say that it must be a perfect square.

I have explained the why and how of each one of these statements in this post: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2010/12 ... t-squares/
You wouldn't need to "learn" anything once you go through it.


KarishmaB
Hi my friend! Unfortunately, I could not access the link that you shared. Would you be able to share more information on this form?

I was a bit confused because I learned "an odd number of factors=a perfect square".

So, if I take the square root of 4 --> 4^(1/2)=2*2 -->2 --> because there is only one integer, that makes a perfect square?

Thank you for all of your time.
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Re: Perfect square [#permalink]
10 Sep 2022, 07:39
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