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M14-04

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Math Expert
Joined: 02 Sep 2009
Posts: 49496
M14-04  [#permalink]

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16 Sep 2014, 00:50
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Difficulty:

45% (medium)

Question Stats:

61% (00:55) correct 39% (01:09) wrong based on 92 sessions

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What is the sum of all common divisors of 48 and 36?

A. 22
B. 24
C. 26
D. 27
E. 28

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Math Expert
Joined: 02 Sep 2009
Posts: 49496
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16 Sep 2014, 00:50
2
Official Solution:

What is the sum of all common divisors of 48 and 36?

A. 22
B. 24
C. 26
D. 27
E. 28

The common divisors of 48 and 36 are: 1, 2, 3, 4, 6, 12. Their sum is 28.

Answer: E
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Joined: 13 Dec 2015
Posts: 4
Re: M14-04  [#permalink]

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05 Sep 2016, 20:13
Hello, what is the shortest working out steps to find the common divisor?
Intern
Joined: 07 Feb 2016
Posts: 21
GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39
Re: M14-04  [#permalink]

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07 May 2017, 01:39
unleesooj wrote:
Hello, what is the shortest working out steps to find the common divisor?

I did prime factorization in order to calculate the number of factors:

$$48=2^4*3^1$$

$$factors=5*2=10$$

and then divided 48 by ascending numbers:
$$48/1$$
$$48/2$$
$$48/3$$
$$48/4$$
$$...$$

This took me 2:15 for this question. Nevertheless, the very first step is not necessary, it was helping me not to forget any factor.
Manager
Joined: 14 May 2015
Posts: 52
Re: M14-04  [#permalink]

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07 May 2017, 03:17
36=1,2,3,4,6,9,12,18,36
48=1,2,3,4,6,8,12,16,24,48
common sum=1+2+3+4+6+12=28
ans: E
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Joined: 04 Apr 2017
Posts: 18
Re: M14-04  [#permalink]

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16 Jun 2017, 11:59
1. Find the GCD of the numbers
2. Factors of GCD are also factors of the two numbers -> List out all the factors of the GCD.
3. Sum them up.
Intern
Joined: 13 Jun 2015
Posts: 9
M14-04  [#permalink]

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23 Aug 2018, 06:36
Quote:
1. Find the GCD of the numbers
2. Factors of GCD are also factors of the two numbers -> List out all the factors of the GCD.
3. Sum them up.

Bunuel
Could you please confirm whether the above method should hold true for general cases? IMO the GCD should have all the common factors of a list of numbers. And there is that general formula to calculate the sum of all factors of a number, using which we can calculate the sum of factors of GCD. This should ideally provide a generic method to arrive at the sum of common factors for all numbers?
Please correct me if I am mistaken.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 49496
Re: M14-04  [#permalink]

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23 Aug 2018, 22:52
1
shubhajit wrote:
Quote:
1. Find the GCD of the numbers
2. Factors of GCD are also factors of the two numbers -> List out all the factors of the GCD.
3. Sum them up.

Bunuel
Could you please confirm whether the above method should hold true for general cases? IMO the GCD should have all the common factors of a list of numbers. And there is that general formula to calculate the sum of all factors of a number, using which we can calculate the sum of factors of GCD. This should ideally provide a generic method to arrive at the sum of common factors for all numbers?
Please correct me if I am mistaken.

Thanks

_____________________________
Yes, that approach is generally true.
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Re: M14-04 &nbs [#permalink] 23 Aug 2018, 22:52
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