P is a natural number. 2P has 28 divisors and 3P has 30 divisors. How many divisors of 6P will be there?
  • a)
    35    
  • b)
    40    
  • c)
    45    
  • d)
    48
Correct answer is option 'A'. Can you explain this answer?

Quant Question

Nithin Bharadwaj
Sep 19, 2019

Dinesh Kukreja
Jun 11, 2018
Solution 1:
2P is having 28(4*7) divisors but 3P is not having a total divisors which is divisible by 7, so the first part of the number P will be 2^5.
Similarly, 3P is having 30 (3*10) divisors but 2P does not have a total divisors which is divisible by 3. So 2nd part of the number P will be 3^3. So, P = 2^5*3^3 and the solution is 35.

Solution 2:
2P has 28 divisors =4x7,
3P has 30 divisors
Hence P=2^5 3^3
6p =2^6 3^4
Hence 35 divisors

Rahul Prajapati
Aug 13, 2019
Solution doesn't satisfie, can someone solve this correctly.

Dhanaraj S
Jul 25, 2020
Coming to concepts of prime factorization

any number can be expressed as powers of products of prime numbers ,
also the thing to note is that, the number of divisors of a number thus can be obtained by this prime factorization, which is product of (powers+1)
let a=2^a*3^b....
so no of divisor =( a+1)(b+1)....

here let
p has r divisor
r=(a+1)(b+1)k
28=(a+2)(b+1)k. where k is contribution from other primes than 2 and 3

similarly,
30 =(a+1)(b+2)k
by trial and error
28=1*4*7
30=1*6*5
thus x=5
y =3
k=1
so 3p has (a+2)(b+2)k divisor
=35 divisor

Jyothi Sai
Jan 04, 2020
How you write 2p and 3p....will you please give any explanation....

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