A natural number has exactly 10 divisors including 1 and itself. How many distinct prime factors can this natural number have?

A. Either 1 or 2

B. Either 1 or 3

C. Either 2 or 3

D. Either 1,2 or 3

• Either 1 or 2
  Reason : since given maximum factors is 10...this is obtained only by (9+1) or (4+1)*(1+1)
  
  Since we know that for p1^a,p2^b.... are factors ,p1 and p2 are prime...then total factors are (a+1)*(a+2)....
  
  by this way we can't split 10 not more than 2 ways...so answer is i or 2
• 9 years agoHelpfull: Yes(39) No(0)
• since we know that if a,b is prime factor of a number n.
  and n=a^p*b^q
  then number of divisor=(p+1)(q+1).
  here given 10 divisor so possible factor of 10 is 1,10 or 2,5
  so no of prime factors is either 1 or 2
• 9 years agoHelpfull: Yes(24) No(0)
• let us take 120 = 1x2x3x4x5x6x8x10x12x120
  
  here it have 3 prime factors
• 9 years agoHelpfull: Yes(2) No(26)
• c is the correct answer
• 9 years agoHelpfull: Yes(0) No(13)
• a,as a^p*b^q gives (p+1)*(q+1)
• 9 years agoHelpfull: Yes(0) No(3)