Latest TCS Aptitude Question SOLUTION: if N is a natural no and N^3 has 16 factors then how many maximum factors can N^4 have??a)21 b)24 c)25 d)26

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(#M40011304) TCS Logical Reasoning question Keep an EYE

if N is a natural no and N^3 has 16 factors then how many maximum factors can N^4 have??a)21 b)24 c)25 d)26

Asked In TCS urvashi (11 years ago)

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RIMAN  (11 years ago)

lets say a term 6
Now 6^3=(2^3 )* (3^3)
so, no of factors=(3+1)*(3+1)=16(using prime factorization)
Now similarly
6^4=(2^4)*(3^4)
so factors, (4+1)*(4+1)= 25
So the ans is c)25

Is this solution Helpfull? Yes (50) | No (7)  

Anton Menezes  (10 years ago)

Consider n = a x b, where a and b are 2 prime factors of n.
Hence, n^3 = a^3 x b^3. In this case, n^3 will have a total of 4 x 4 = 16 factors.
Note: The number of factors of a number which can be represented as N = a^p x b^q x c^r , where a, b, c are prime numbers is (p+1)(q+1)(r+1)
Hence, the number n can be represented only as a product of two prime factors.
Similarly, n^4 = a^4 x b^4. In this case n^4 will have 5 x 5 = 25 factors.

Is this solution Helpfull? Yes (10) | No   

lala  (11 years ago)

let....n^3= x^3*y^3........then no/ of factor = (3+1)(3+1)is 16 or possible case
n^4 = x^4*y^4 = (4+1)(4+1)=25
one case can also be possible for n^3 let 16 having factor like 2*8 but i think this is impossible case..so only 4*4 case is possible for n^3 having 16 factor.....

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urvashi  (11 years ago)

how????? can u plz explain??

Is this solution Helpfull? Yes (6) | No (4)  

Divyansh jaiswal  (8 years ago)

if n=32,ans is 21........ if n=6 ans is 25,,,,,,ambiguity is there

Is this solution Helpfull? Yes (3) | No (2)  

Garima  (11 years ago)

N^4 can have 25 factors.

Is this solution Helpfull? Yes (2) | No (4)  

SOLAIRAJA  (7 years ago)

n^y=(y+1)^×
4^x=16
x=2
(4+1)^2=25

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jaiky kumar  (4 years ago)

Total factors of a number N=
a
p
.
b
q
.
c
r
.
.
.
is (p+1)(q+1)(r+1)...
As
n
3
has 16 factors
n
3
can be one of the two formats given below
n
3
=
a
15

n
3
=
a
3
.
b
3

If
n
3
=
a
15
then n =
a
5
and number of factors of
n
4
= 21
n
3
=
a
3
.
b
3
then n = ab and number of factors
n
4
= 25

Is this solution Helpfull? Yes | No   

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