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

Question

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

niks18 · Accepted Answer

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

EgmatQuantExpert · Answer

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. ………….. 
• 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………..   
• 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 …………….   
• Substituting the values obtained in   and   in equation  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.

Jansaida · Answer

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

ortizmoj · Answer

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 ?????

GmatDaddy · Answer

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.

bumpbot · Answer

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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?

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