Given a number N, 2*N has 28 factors and 3*N has 30 factors. Calculate how many factors will be there in 6*N?

• 28=7*4
  30=6*5 therefore 2N=2^6*3^3
  and 3N=2^5*3^4
  therfore 6N=2^6*3^4
  so no. of factors are 7*5=35.
  
  ans is 35
• 11 years agoHelpfull: Yes(21) No(9)
• Ans. 35
  
  N => 2^a + 3^b + k^c ; k^c = 5^d + 7^e + ......
  2*N => 2^(a+1) + 3^b + k^c
  3*N => 2^a + 3^(b+1) + k^c
  
  now,
  (a+1)*b*c = 28 & a(b+1)c = 30,
  so only possible combination of (a,b,c) is (6,4,0)
  coz, in case of 2*N,
  (6+1)*4=28
  & in case of 3*N,
  6*(4+1)=30;
  So, 6*N => (a+1)*(b+1) = (6+1)*(4+1)=35..
• 11 years agoHelpfull: Yes(15) No(2)
• 28=7*4
  so the solution is as follows
  30=6*5 ; 2N=2^6*3^3
  and 3N=2^5*3^4
  6N=2^6*3^4
  so no. of factors are 7*5=35.
• 11 years agoHelpfull: Yes(3) No(2)
• 35 is right ans
• 11 years agoHelpfull: Yes(2) No(2)
• ans-32
  as no. of factor for N is 26
  when 2 is multiplied-- it increases by 2 (unless 2*N is not a square).
  when 3 is multiplied-- it increases by 4 (unless 3*N is not a square).
  same for when 6 multiplied-- it increases by 6 (unless 6*N is not a square).
  if square then Ans =31
  
• 11 years agoHelpfull: Yes(1) No(11)