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How many factors, of the number 1080, are a multiple of 2?

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How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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New post Updated on: 13 Aug 2018, 01:58
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e-GMAT Question:



How many factors, of the number 1080, are a multiple of 2?

    A) 10
    B) 12
    C) 16
    D) 24
    E) 32

This is

Question 2 of The e-GMAT Number Properties Marathon




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Question 3 of the Marathon


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Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:54.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:58, edited 3 times in total.
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Re: How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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New post 27 Feb 2018, 11:24
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EgmatQuantExpert wrote:

Question:



How many factors, of the number 1080, are a multiple of 2?

    A) 10
    B) 12
    C) 16
    D) 24
    E) 32


\(1080=2^3*3^3*5\)

total number of factors of \(1080 = (3+1)*(3+1)*(1+1)=32\)

Factors that are odd will be formed from \(3^3*5\). Hence total number of odd factors \(= (3+1)*(1+1)=8\)

Therefore total number of even factors (or multiples of 2) \(= 32-8=24\)

Option D
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Re: How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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New post 28 Feb 2018, 00:54

Solution:



    • Let us first apply prime factorization and express these numbers in terms of it prime factors. \(1080 = 2*2*2*3*3*3*5\)
      o This can be written as:
         \(1080 = 2^3 * 3^3 * 5\)
    • As mentioned before, any factors which are a multiple of \(2\), has to be even and hence we are simply looking for even factors of the number \(1080\).
    • But how do we find the number of even factors?
      o Per our conceptual knowledge, we know that a number can have either odd factors or even factors or both.
      o Thus, the total factors of any number have to be a combination of only these two types of factors.
         Total factors = Even Factors + Odd factors
    • Since we need even factors, we can re-arrange and write the formula as follows:
    • Even factors = Total factors – Odd factors. …………..[I]
    • Per our conceptual understanding,
      o Total factors of \(1080\)= (Power of 2 +1) * (Power of 3+1) * (Power of 5+1)
         Total factors = \((3+1) * (3+1) * (1+1)\)
         Total factors = \(4 * 4 * 2 = 32\) factors………..[II]
    • Total odd factors of \(1080\) can be found out using the powers of \(3\) and \(5\) only. we cannot include \(2\) as that would give us even factors
      o So, odd factors of \(1080\) = (Power of 3+1) * (Power of 5 +1)
         Odd Factors = \((3+1) * (1+1)\)
         Odd Factors = \(4 * 2 = 8\) factors …………….[III]
    • Substituting the values obtained in [II] and [III] in equation [I]we get:
      o Even factors = Total Factors – Odd Factors
         Even factors = \(32- 8\)
         \(24\) factors
The number of factors of \(1080\) which are multiples of \(2\) is equal to \(24\), and hence the correct answer is Option D.
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Re: How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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New post 19 Mar 2018, 02:25
EgmatQuantExpert wrote:

e-GMAT Question:



How many factors, of the number 1080, are a multiple of 2?

    A) 10
    B) 12
    C) 16
    D) 24
    E) 32

This is

Question 2 of The e-GMAT Number Properties Marathon




Go to

Question 3 of the Marathon




Hello
I don't know whether my approach is correct, but ya when we factorize 1080 it will boil down to 2^3 * 3^3 * 5. For any number to be a multiple of 2, It must contain at least 2 in it. so in this case 2^0=1 is not acceptable. 2^1,2^2,2^3 are acceptable. All the factors of 3 and 5 are acceptable. so the number of factors are 3*4*2= 24
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Re: How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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New post 20 Sep 2018, 19:52
Can you please let me know what is going on here?
I literally dont know where is the

"(Power of 2 +1) * (Power of 3+1) * (Power of 5+1)
 Total factors = (3+1)∗(3+1)∗(1+1)"

coming from ?????
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Re: How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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New post 21 Sep 2018, 00:30
ortizmoj wrote:
Can you please let me know what is going on here?
I literally dont know where is the

"(Power of 2 +1) * (Power of 3+1) * (Power of 5+1)
 Total factors = (3+1)∗(3+1)∗(1+1)"

coming from ?????


This is a general rule to calculate the total no of factors of a number from its prime factors.
If a number N has a, b and C as its prime factors such that
\(N=(a^p)*(b^q)*(c^r)\)
Then the total no of factors of N will be \((p+1)*(q+1)*(r+1)\)
This will include 1 and the number it self.
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Re: How many factors, of the number 1080, are a multiple of 2? &nbs [#permalink] 21 Sep 2018, 00:30
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How many factors, of the number 1080, are a multiple of 2?

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