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

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Joined: 04 Jan 2015
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How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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Updated on: 13 Aug 2018, 01:58
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Difficulty:

65% (hard)

Question Stats:

48% (01:39) correct 52% (01:53) wrong based on 183 sessions

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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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27 Feb 2018, 11:24
2
3
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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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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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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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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Posts: 268
Re: How many factors, of the number 1080, are a multiple of 2?  [#permalink]

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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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