Latest TCS Aptitude Question SOLUTION: A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have?

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A number has exactly 3 prime factors, 125 factors of this number are perfect squares and 27 factors of this number are perfect cubes. overall how many factors does the number have???

Asked In TCS deepak gupta (11 years ago)

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kck  (11 years ago)

As it is given no has three prime factors....
so we may consider it as N=(A^p)(B^q)(C^r)
now total no of factors of this no is
(p+1)(q+1)(r+1).
and no of square factors =([p/2] +1)([q/2] +1)([r/2] +1)
and no of cubic factors =([p]/3 +1)([q]/3 +1)([r]/3 +1)
but it is given that the no has 125 square factors i.e
([p/2] +1)([q/2] +1)([r/2] +1)=125
=> [p/2]=4.....[r/2]=4
=> p=8,q=8 nd r=8
similarly for cubic factor
([p/3] +1)([q/3] +1)([r/3] +1)=27
[p/3]+1=3,[q/3]+1=3 nd [r/2]+1=3
=> [p/3]=2=[q/3]=[r/3]
possible values of p,q,r will be 6,7 or 8
now total no of factors =(8+1)(8+1)(8+1)=729
hence answer is 729
Note:here [X ] means greatest intigr value , either equal to or less than X.

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Akash Soni  (11 years ago)

Answer for this question is 729
the explanation goes like this
Let a,b,c be three prime no.
since the no. of perfect square as a factor is 125
which can only be if every prime no. has power in the multiple of 2 including zeros(bcoz any no. to the power of zero is a perfect square)
so power must be 0,2,4,6,8
thereby 5*5*5=125
Since no. of cube as a factor is 27
therefore power in the prime no. will be in the multiple of 3
so power are 0,3,6
hence the no. N=a^8*b^8*c^8
hence total no. of factor is (8+1)(8+1)(8+1)=729

Is this solution Helpfull? Yes (22) | No (37)  

neha parween  (11 years ago)

unable to understand

Is this solution Helpfull? Yes (17) | No (2)  

Harish Singh Bohra  (11 years ago)

125*2=250
27*3=81
3 prime factor= 5 factor 1 and no it self
=250+81+5
336

Is this solution Helpfull? Yes (4) | No (23)  

SHANU MAHAJAN  (11 years ago)

hey akash i am unable to understand your logic can u be more clear

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

Santosh Kumar M S  (11 years ago)

send that ans clearly

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raunaque.afroz  (9 years ago)

kck plz xplain me the solution..

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