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M04-31

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M04-31  [#permalink]

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New post 16 Sep 2014, 00:23
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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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New post 16 Sep 2014, 00:23
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

\(28 = 1+2+4+7+14\)


Answer: C
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Re: M04-31  [#permalink]

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New post 04 Oct 2014, 10:57
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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Re: M04-31  [#permalink]

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New post 04 Oct 2014, 11:11
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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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Re: M04-31  [#permalink]

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New post 16 Nov 2014, 16:55
So when it says "unique factors' - that does not equal prime?
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New post 17 Nov 2014, 02:01
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Re: M04-31  [#permalink]

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New post 09 Sep 2016, 07:23
Bunuel wrote:
Official Solution:


\(28 = 1+2+4+7+14\)


Answer: C


Why 12 is incorrect 1+2+3+6 = 12
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New post 09 Sep 2016, 08:04
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Re: M04-31  [#permalink]

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New post 03 Mar 2018, 15:56
Bunuel, any way to narrow down some options, so it wont be 100% try and error?
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Re: M04-31  [#permalink]

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New post 05 Aug 2018, 06:47
Is there a faster way to find ALL the factors of a number?
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New post 05 Aug 2018, 07:14
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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



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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M04-31 &nbs [#permalink] 05 Aug 2018, 07:14
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