Latest TCS Aptitude Question SOLUTION: The prime factorization of integer N is A*A*B*C where A, B and C are all distinct prime integers. How many factors does N have? a)12 b)24 c)4 d)6

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The prime factorization of integer N is A*A*B*C where A, B and C are all distinct prime integers. How many factors does N have?
a)12
b)24
c)4
d)6

Asked In TCS krishnaprasad TATA (11 years ago)

Unsolved Read Solution (12)

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PARAG KAMRA  (11 years ago)

n is A*A*B*C =A^2*B*C
no. of factors=(2+1)(1+1)(1+1)
=12
REASON:- A HAS POWER OF 2,B HAS POWER OF 1,C HAS POWER 1
SO PRIME FACTORIZATION CAN BE CALCULATED AS:
IF A^P+B^Q+C^R,THEN
PRIME FACTORIZATION IS (P+1)*(Q+1)*(R+1)
SO IN THIS CASE P=2,Q=1,R=1
SO (2+1)(1+1)(1+1)=12 FACTORS(ANS)

Is this solution Helpfull? Yes (83) | No (2)  

PARAG KAMRA  (11 years ago)

n is A*A*B*C =A^2*B*C
no. of factors=(2+1)(1+1)(1+1)
=12

Is this solution Helpfull? Yes (7) | No (5)  

Nandhini  (11 years ago)

the prime factorization of integer n is (a^p)*(b^q)*(c^r)

so the number of factors of n will be expressed by the formula (p+1)*(q+1)*(r+1)

given the prime factorization of integer n is (a^2)*(b^1)*(c^1)
so the number of factors of n = (2+1)*(1+1)*(1+1) = 3*2*2 = 12

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

PARAG KAMRA  (11 years ago)

IN THIS QUES WE CAL ALSO TAKE
A=2,B=1,C=3
THEN 2^2*1*3=12 FACTORS

Is this solution Helpfull? Yes (2) | No (5)  

Garima  (11 years ago)

12

N will have 3*2*2 = 12 factors.

Is this solution Helpfull? Yes (1) | No (9)  

shyamjee kumar  (11 years ago)

12 factors.
3+3+3+3=12 factors.

Is this solution Helpfull? Yes (1) | No (4)  

sahasra  (11 years ago)

can you please explain the solution clearly..@parag kamra

Is this solution Helpfull? Yes (1) | No (3)  

PARAG KAMRA  (11 years ago)

A=1,B=2,C=3
(1+1)*2*3=12 FACTORS

Is this solution Helpfull? Yes (1) | No (8)  

sahasra  (11 years ago)

thank you..@parag kamra

Is this solution Helpfull? Yes (1) | No (8)  

sumit jindal  (11 years ago)

if n=a^p*b^q*c^r
then no. of factors=(p+1)(q+1)(r+1)-1
so (2+1)(1+1)(1+1)-1= 11 ans

Is this solution Helpfull? Yes | No (4)  

Puja Bhowmick  (8 years ago)

GIVEN N=A*A*B*C
N=(A^2)*(B^1)*(C^1)

PRIME FACTORIZATION OF N= (A^P)*(B^Q)*(C^R) WHERE P,Q,R ARE PRIME FACTORS
NUMBER OF FACTORS OF N WILL BE EXPRESSED AS = (P+1)*(Q+1)*(R+1)
HERE P=2, Q=1, R=1
(2+1)*(1+1)*(1+1)=12
ANS-: 12

Is this solution Helpfull? Yes | No (1)  

raja mondal  (8 years ago)

answer 24

2*(!4/!2)

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