How many 3-digit numbers have even number of factors?(a) 22 (b) 879 (c) 21 (d) 878

• Every factor of a number has a pair, so there ought to be an even number of factors for every number. However, if a pair of the factors are the same number, then there will be an odd number of factors, that is if the number is a perfect square.
  
  Assuming three digit numbers are 100 to 999:
  
  From 100 to 999, the perfect squares are 10^2 = 100 to 31^2 = 961, a total of 31-10+1 = 22 numbers.
  
  So of the 999-100+1 = 900 three digit numbers, 22 have an odd number of factors, so 900-22 = 878 have an even number of factors.
• 12 years agoHelpfull: Yes(20) No(2)
• Every factor of a number has a pair, so there ought to be an even number of factors for every number. However, if a pair of the factors are the same number, then there will be an odd number of factors, that is if the number is a perfect square.
  
  Assuming three digit numbers are 100 to 999:
  
  From 100 to 999, the perfect squares are 102 = 100 to 312 = 961, a total of 31-10+1 = 22 numbers.
  
  So of the 999-100+1 = 900 three digit numbers, 22 have an odd number of factors, so 900-22 = 878 have an even number of factors.
• 12 years agoHelpfull: Yes(9) No(3)
• option (d )........878 ( 900-22).... 3-digit numbers have even number of factors.
  Because there are 22 perfect squares between 100-999.
• 12 years agoHelpfull: Yes(5) No(4)
• plz plz explain it
• 12 years agoHelpfull: Yes(4) No(1)
• please explain the logic clearly...how is 22 perfect squares and why did u subtracted from 900
• 12 years agoHelpfull: Yes(3) No(2)
• perfect sq always have odd no of factor..
  like 36
  36=6^2 = 2^2*3^2
  so, no of factors = [ 2+1]*[2+1] =9
  which is odd.. chechk others if u want...
  answer is 900-22= 878
• 12 years agoHelpfull: Yes(2) No(0)
• Hell No! Only the prime numbers have even number of factors so the answer is (a)22 (from 10^2 to 31^2)
• 12 years agoHelpfull: Yes(0) No(1)
• Sorry for my previous answer the correct answer is 878 because i've counted 1 as a factor
• 12 years agoHelpfull: Yes(0) No(0)
• nice one...agree with abhishek verma
• 11 years agoHelpfull: Yes(0) No(0)