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?

• he says 2*N has 28 factors - i considered N to be made of 2,3 prime factors.
  Therefore 2*N = 2^6 * 3^3 (#note my original number N = 2^5 * 3^3)
  only then the number of factors = (6+1) * (3+1)= 7 * 4= 28
  now check for 2nd condition 3* N = 2^5 * 3^4 = (5+1)*(4+1)= 6*5=30
  therfore my assumption was correct now u can find for 6* N = 2^6 * 3^4=(7)*(5) = 35
• 10 years agoHelpfull: Yes(16) No(1)
• 7*5=35
  n=(3^6)(2^4)
• 10 years agoHelpfull: Yes(8) No(1)
• Let
  N=2^x * 3^y * 5^z * 7^a * 11^b *...
  
  2*N= 2^(x+1) * 3^y * 5^z * 7^a * 11^b *... ,No. of factors= F1=(x+2) * (y+1) * (z+1) * (a+1) * (b+1) * ..
  
  3*N= 2^x * 3^(y+1) * 5^z * 7^a * 11^b *..., No. of factors= F2=(x+1) * (y+2) * (z+1) * (a+1) * (b+1) * ..
  
  
  now factorize 28 and 30
  28=(2*2*7) or (4*7)
  30=(2*3*5) or (6*5)
  
  we see that both have maximum three factors. so we can write the numbers in this form
  
  2*N= 2^(x+1) * 3^y * 5^z , and No. of factors= F1=(x+2) * (y+1) * (z+1)= 28 ----------(1)
  
  3*N= 2^x * 3^(y+1) * 5^z , and No. of factors= F2=(x+1) * (y+2) * (z+1) = 30------------(2)
  
  After this point we have to only check for which values of x,y, or z satisfy the both conditions. for this factorize anyone and put the values of x,y,z in the second equation.
  
  now, F2=30 can factorized in (2*3*5) or (6*5)
  
  case 1: F2= 2*3*5=(x+1) * (y+2) * (z+1)
  so, x=1, y=1, z=4
  now put the values of x,y,z in F1
  F1= (x+2) * (y+1) * (z+1)=3*2*5=30 !=28,, this is not possible
  
  case 2: F2= 6*5=(x+1) * (y+2)
  so, x= 5, y=3
  now put the values of x, y in F1
  
  F1=(x+2) * (y+1) = (5+2)*(3+1)= 28.
  
  now 6*N= 2*3* N= 2^(x+1) * 3^(y+1)= 2^6 * 3^4.
  
  so no. of factors =(6+1)*(4+1)= 7*5= 35
• 10 years agoHelpfull: Yes(8) No(2)
• Can U explain how u got that answer??
• 10 years agoHelpfull: Yes(0) No(6)
• 2,3 are factors of 6
  so
  6*n has 28+30=58 factors
• 10 years agoHelpfull: Yes(0) No(12)
• right ans is 42
  take n=864 and check it
• 10 years agoHelpfull: Yes(0) No(6)
• i think so the ans is 30
• 10 years agoHelpfull: Yes(0) No(5)
• N and 2^n gives 28 which means that there is no factor of 2 in n. So the number of factors is 30
• 9 years agoHelpfull: Yes(0) No(0)