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# M04-31

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:23
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35% (medium)

Question Stats:

71% (01:10) correct 29% (01:20) wrong based on 189 sessions

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A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$. Which of the following is also a perfect number?

A. 12
B. 20
C. 28
D. 48
E. 60

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Joined: 02 Sep 2009
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15 Sep 2014, 23:23
Official Solution:

A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$. Which of the following is also a perfect number?

A. 12
B. 20
C. 28
D. 48
E. 60

$$28 = 1+2+4+7+14$$

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04 Oct 2014, 09:57
How we have calculated Factor of 28 ? 4 and 14 are not prime .. is it correct to show factor as non prime number ?
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04 Oct 2014, 10:11
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rahulgmat2014 wrote:
How we have calculated Factor of 28 ? 4 and 14 are not prime .. is it correct to show factor as non prime number ?

Factor of an integer is not necessarily a prime number.

A divisor of an integer $$n$$, also called a factor of $$n$$, is an integer which evenly divides $$n$$ without leaving a remainder. In general, it is said $$m$$ is a factor of $$n$$, for non-zero integers $$m$$ and $$n$$, if there exists an integer $$k$$ such that $$n = km$$.

So, the factors of 28 are 1, 2, 4, 7, 14, and 28.

Theory on Number Properties: math-number-theory-88376.html
Divisibility tips: divisibility-multiples-factors-tips-and-hints-174998.html?hilit=divisibility%20tips

DS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=354
PS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=185[/textarea]

Hope it helps.
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16 Nov 2014, 15:55
So when it says "unique factors' - that does not equal prime?
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17 Nov 2014, 01:01
1
phferr1984 wrote:
So when it says "unique factors' - that does not equal prime?

No, Unique factors = different factors.
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09 Sep 2016, 06:23
Bunuel wrote:
Official Solution:

$$28 = 1+2+4+7+14$$

Why 12 is incorrect 1+2+3+6 = 12
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09 Sep 2016, 07:04
vs224 wrote:
Bunuel wrote:
Official Solution:

$$28 = 1+2+4+7+14$$

Why 12 is incorrect 1+2+3+6 = 12

4 is also a factor of 12.
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03 Mar 2018, 14:56
Bunuel, any way to narrow down some options, so it wont be 100% try and error?
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05 Aug 2018, 05:47
Is there a faster way to find ALL the factors of a number?
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05 Aug 2018, 06:14
1
imran1994 wrote:
Is there a faster way to find ALL the factors of a number?

Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

2. Properties of Integers

5. Divisibility/Multiples/Factors

For other subjects:
ALL YOU NEED FOR QUANT ! ! !
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30 Nov 2018, 07:23
Bunuel wrote:
A perfect number is defined as one for which the sum of all the unique factors less the number itself is equal to the number. For instance, 6 is a perfect number, because the factors of 6 (apart from 6 itself) are 1, 2 and 3, and $$1 + 2 + 3 = 6$$. Which of the following is also a perfect number?

A. 12
B. 20
C. 28
D. 48
E. 60

This is question is simple to calculate for all , To calculate sum of factors except the number , we calculate sum of all factors - the number.

Sum of all factors of a number is given by if a number is P= a^n * b^m * c^k. Sum of all factors of P = (1 + a ..... a^n) (1+b+b^2 .... b^m )(1+c + c^2+....c^k)

so 28 will have (1+ 2 + 4) (1+ 7) = 56 sum of factors ,excluding number will be 28, so the perfect number.
Re: M04-31 &nbs [#permalink] 30 Nov 2018, 07:23
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# M04-31

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