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How many factors, of the number 1080, are a multiple of 2?
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Updated on: 13 Aug 2018, 00:58
Question Stats:
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Re: How many factors, of the number 1080, are a multiple of 2?
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27 Feb 2018, 10:24
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) \(= 328=24\) Option D




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Re: How many factors, of the number 1080, are a multiple of 2?
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27 Feb 2018, 23:54
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 rearrange 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?
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19 Mar 2018, 01:25
EgmatQuantExpert wrote: eGMAT 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 eGMAT 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?
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20 Sep 2018, 18:52
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?
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20 Sep 2018, 23:30
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
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