How many factors of the number 2^3 x 3 x 5^2 are even?

Question

e-GMAT Question:

How many factors of the number  2^3 * 3 * 5^2  are even?

A) 10
B) 12
C) 16
D) 18
E) 24

This is  Question 2 of  The e-GMAT Number Properties Marathon

Go to   Question 3 of the Marathon

Kritesh · Answer

The total no: of factors are denoted by (p+1)(q+1)(r+1). Therefore it would be 4*2*3 = 24

Lets remove the powers of 2 as they give even factors , then we have 3*5^2 ,which has 2*3= 6 factors

To get the even no: of factors we need to subtract the odd no: of factors from the total , that is 24-6=18 even factors.

Hence answer is option D .

CHIRANJIV87C · Answer

D) 18

Total no. factors = 4x2x3 = 24
Now the no. of factors that will be odd will have no multiple of hence count the factors which are without 2, = 2x3 = 6

Therefore no. of even factors = 24 - 6 = 18

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rkishores051 · Answer

2^3 * 3 *5^2

number of even factors = 3*(1+1)*(2+1)= 3*2*3=18
The first 3 comes from the 2 with power 1 and obove (2^1, 2^2, 2^3)

Answer: D

EgmatQuantExpert · Answer

Solution:

A factor of a number can either be  even  or  odd .
Hence, we can write: 
  Total factors of a number = Even factors of the number + Odd factors of the number. 
  Total number of factors in  2^3 * 3 * 5^2  =  (3+1) * (1+1) * (2+1)  = 4*2*3  =  24 .    From our conceptual knowledge, any number written in its prime factorized form will have odd factors only if all the prime factors of the numbers are odd.  
 Similarly, here in this question, only  3  and  5  are such prime factors of the number. 
 Odd factors in  2^3 * 3 * 5^2  = number of factors in  3 * 5^2  =  (1+1) * (2+1) = 6     
 Since the number of odd factors of  2^3 * 3 * 5^2  is  6 , and we already have the total number of factors to be  24 , the number of even factors of  2^3 * 3 * 5^2 = 24-6 = 18  
Hence, the correct answer is Option D.

philipssonicare · Answer

I tried to double-check when solving by using the manual way. 24 minus the factors
3, 5, 15, 25, 75
But this makes 19. I couldn't reconcile this for much too long.

Do not forget that  1  is a factor!

pk123 · Answer

2^3* 3*5^2
factors of which can be written as 2^0 *(3*5^2) which is nothing but 1*(3*5^2)
2^1 *( 3*5^2)
2^2 *(3*5^2)
2^3*(3*5^2)
and for each of the above 3*5^2 will have (1+1)*(2+1) factors, so total number of factors is 6....
So for every (2^0, 2^1, 2^2 and 2^3) there are 6 combinations...
So for even factors at least one 2 should be present which gives 6*3 =18 factors

Now while calculating 6 factors for each 2 series we have already counted when each of them becomes 0
i.e Factors of 3*5^2 can be thought of (3^0*5^0=1, 3^0*5=5, 3^0*5^2=25, 3*5^0=3, 3*5^1=15, 3*5^2=75), so 6 factors are (1,5,25,3,15,75)
so 1 gets accounted in 6 factors of 3*5^2

Kratosgmat · Answer

total factors = 4*2*3 = 24
Number of odd factors = 2*3=6
therefore even = 24-6=18

gmatophobia · Answer

As we require even factors we need to ensure that the factors have at least one-two, put otherwise, we have to discount the possibility of  2^0

Number of even factors =  3 * 2 * 3 = 18

Option D

bumpbot · Answer

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How many factors of the number 2^3 x 3 x 5^2 are even?

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