Latest MBA Aptitude Question SOLUTION: how many natural numbers are there with 24 factors where 2,3 and 5 are the only prime factors?

1) 36
2) 27
3) 12
4) 9

• Placement Papers
• /
• MBA
• /
• Numerical Ability
• /
• Number System

MBA Question Papers:

(#M40016599) MBA Numerical Ability question number systems, progressions Keep an EYE

how many natural numbers are there with 24 factors where 2,3 and 5 are the only prime factors?

1) 36
2) 27
3) 12
4) 9

Asked In MBA (11 years ago)

Unsolved Read Solution (2)

Is this Puzzle helpful?   (5)   (3) Submit Your Solution Number System

Read Solution (2) :

tejashwi kumar  (10 years ago)

24=2^3*3
These powers have to be distributed in 3 places…
A+b+c=3 has 10 soln
X+y+z=1 has 3 soln
Net =10*3=30 but here 2,2,6 is also included 3 times..hence ans =30-3=27

Is this solution Helpfull? Yes (1) | No (2)  

suyash jadhav  (7 years ago)

number of factors =(m+1)*(n+1)*(c+1)
24=2*3*4
=2*2*6
with prime numbers as 2,3 and 5. using permutation and combination
2^1*3^2*5^3 can be arranged in 6 different ways
similarly, 2^3*3^1*5^2 can be arranged in 6 different ways
2^3*3^2*5^1 can be in 6 different ways.
and 2^2*3^3*5^1 can be in 6 different ways.
and similarly, 2*2*6 can be in 3 different ways.
so 6+6+6+6+3=27

Is this solution Helpfull? Yes | No (1)  

Please Login to Read Solution.