A number number has exactly 10 divisor including 1 and itself. How many distinct prime factor can this natural number have ?please tag me

1) 1 or 2
2) 1 or 3
3) 2 or 3
4) either 1,2 or 3

• Check on 29 i.e 512 , 39, 59 which have only 1 prime factor and 80 , 48 which are having 2
  
  prime factors and total of 10 divisors.
  
  Let us also consider the case of 3 prime factors. Let x, y ,z be the three prime factors of a
  
  number. Therefore 1 , x ,y ,z ,xy ,yx, zx ,xyz must be the factors of that nos . We have
  
  minimum 8 such factors with xyz as the nos or the factor of the nos.
  
  When xyz is the nos then we will have exactly 8 divisors but if the nos is greater thn xyz that
  
  is a multiple of xyz , either the nos is multiplied by any of these prime factors x , y , z then
  
  we will get at least 12 divisors. So we don’t get 3 prime factors with 10 divisors.
  
• 9 years agoHelpfull: Yes(0) No(0)