A natural no. has exactly 10 divisors including 1 and itself. how many distinct prime factors can this natural no. have??
Option
a) either 1 or 2
b) either 1 or 3
c) either 2 or 3
d) either 1,2 or 3

• If N=a^p*b^q*c^r... then total number of factors of N =(p+1)(q+1)(r+1) ...
  
  no. of factors =10, two cases are possible
  1) 10=(9+1) => no. will be of form 2^9,3^9,5^9,...etc => 1 prime factor
  
  2) 10=5*2=(4+1)*(1+1) => no. will be of form 2^4*3, 3^4*2, 2^4*5,... etc => 2 distict prime factors
  
  also, suppose if it has 3 distinct factors then total no. of factor will never equal to 10 , we don’t have any no. with 3 prime factors with 10 divisors.
  
  a) either 1 or 2
• 10 years agoHelpfull: Yes(29) No(0)