A number n has some divisor such that 2n has 48 divisors and 3n 30 divisors Find n n is

ans:4725=3*3*3*5*5*7 or 14553=3*3*3*7*7*11
so ans is 27*p1*p1*p2{where p1 or p2 are prime numbers other than 2 1nd 3}
it can be derived in the following way:
number of divisors=(p+1)(q+1)(r+1).... N=a(power p)*b(power q)*c(power r)*....
10 years agoHelpfull: Yes(3) No(8)
suppose the prime factors of the no. are X , Y , Z
when we we multiply 2 to the number we get 48 divisors so factors of 48 are 2*2*2*2*3= 4*2*3*2
when we multiply 3 to the number we get 30 divsors so factors of 30 are
2*3*5= 5*2*3
which means n has factors X with power 3 Y with power 1 and Z with power 2 suc that when 2 is multiplies it becmes (X^0+X^1+X^2+X^3)(Y^0+Y^1)(Z^0+Z^1+Z^2)(2^0+2^1) ie 4*2*3*2=48 factors
now when 3 is multiplied to the number it has 30 factors so X has to be 3 such that on multiplication it becomes (3^0+3^1+3^2+3^3+3^4)(Y^0+Y^1)(Z^0+Z^1+Z^2)= 30 factors
so if we take y to be 5 and z to be 7 next prime no.s we get 6615 as the number
10 years agoHelpfull: Yes(2) No(3)
can any1 plaese refer any link where i can understand this kind of problems.plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz..suggest me a topic atleast
9 years agoHelpfull: Yes(1) No(0)
Revised Sol:So The no is in the form of
N=(3^3)(a^2)(b)
where a and b are the other prime nos other than 2 and 3.
10 years agoHelpfull: Yes(0) No(2)
hai please explain with correct solutions
10 years agoHelpfull: Yes(0) No(2)
Both condition are required to give the right ans.............
9 years agoHelpfull: Yes(0) No(0)

A number n has some divisor such that 2n has 48 divisors and 3n=30 divisors. Find n. n is a non negative number.