a natural numbr has exactly 10 divisors including 1 and itself.how many distint prime factors this natural numbr will have?
options: 1 or2
1 or3
1 or 2or 3
2 or 3

• a) 1 or 2
• 9 years agoHelpfull: Yes(13) No(0)
• Here it is given that the number has exactly 10 divisor including 1 and itself.
  So the number may be (any one prime factors)power 9 .....I.e (2)pow 9, (3)pow 9....etc.total 10 factor=(9+1)=10.
  Also the number may be as (any one prime factors)pow 1*(any one prime factors)pow 4........I.e...(2)pow 1*(3)pow 4...etc= total 10 factor((1+1)*(4+1))=10.
  Hence either 1 or 2 is correct answer.
  
• 9 years agoHelpfull: Yes(6) No(0)
• Formula is : No of Divisor=a*b*c---- Where a-1, b-1, c-1 are no of occurence of that no in factor that no.
  *Ex* - Find no of factor of 40
  40=(2)^3*(5)^1
  so no of factor of 40=(3+1)*(1+1)=8
  Similarly,10=5*2 or(4+1)*(1+1)
  =10*1 (9+1)*(0+1)
  second case is not practical.
  So, X^4*Y^1 is factor of that no.
• 8 years agoHelpfull: Yes(2) No(0)
• Take no as 512 . then the divisors of this no. are
  1,2,4,8,16,32,64,128,256,512;
  
  so only one prime factors are there 2;
  
  Suppose if the number is 48 the divisors are
  1,2,3,4,6,8,12,16,24,48;
  so the prime factors are 2,3;
• 9 years agoHelpfull: Yes(1) No(5)
• 1 or 2 or 3 also possible
• 9 years agoHelpfull: Yes(1) No(2)
• rajesh,,if you could explain how you solved it!!!!!!!!!!!!!
• 9 years agoHelpfull: Yes(0) No(1)
• @rajesh how can u directly take the nos??
  is there any frmula??
• 9 years agoHelpfull: Yes(0) No(1)
• their is direct solution lel 36 as ans it cac factor as 2^2*3^2
  now total sol is (2+1)*(2+1) =9 ie 36 have 9 factor including 1 and 36 itself.
  now since i have no 10 it can only factorise as 2*5 ie(1+1)*(4+1).
  so it have only two soln either 1 or 2. here 1 and 4 shows (x^1*Y^4)
• 9 years agoHelpfull: Yes(0) No(0)
• 2 or 3.would be the ans.512,36,48
• 9 years agoHelpfull: Yes(0) No(2)
• 1 or 2 is the correct answer
• 8 years agoHelpfull: Yes(0) No(0)
• correct answer is
  explanation:
  the factor of 10 =1,2,5,10
  so ans is 1 or 2
• 8 years agoHelpfull: Yes(0) No(1)