How many numbers less than 500 are divisible by 2 or 3 or 4 or 5 or 7 or 21?

• no of prime no's below 500 is 95
  excluding 2,3,5,7, it is 91
  no's not divisible 2,3,4,5,7,21, are
  11*(11,13,17,19,23,29,31,37,41,43) i.e 10
  13*(13,17,19,23,29,31,37) i.e 7
  17*(17,19,23,29) i.e 4
  19*(19,23) i.e 2
  initially 1 is also not divisible
  total = 91+10+7+4+2+1= 115
  answer 500-115 = 385
• 11 years agoHelpfull: Yes(19) No(6)
• first we find the no.s which r not divisible by 2 r 3 r 4 r 5 r 7 r 21.
  all these no.s will be prime no.s.
  since within 100 there r 23 prime no.s which r not devisible by 22 r 3 r 4 r5 r 7 r21. same for 100-200. so total prime no. within 500 will be 115.
  so no.s that r devisible by 2 r 3 r 4 r 5 r 7 r 21 will be 499-115=384.
• 11 years agoHelpfull: Yes(15) No(19)
• @vikas singh : there are 97 prime numbers between 2-499.
  
  so by excluding 2,3,5,7 there will be 93 numbers + 1 (i.e 1 is not divisible by any number). so total 92 numbers which will not divide by these numbers.
  
  so 499-92 = 407.
• 11 years agoHelpfull: Yes(10) No(5)
• @siddanth : could u please explain ur solution....
• 11 years agoHelpfull: Yes(1) No(4)
• div by 2-250
  div by 3-166
  div by 5-100
  div by 7-71
  total-587
  /////no need to find 4, 21
  div by 2&3-83
  div by2&5-50
  div by2&7-35
  div by3&5-33
  div by3&7-23
  total-238
  now
  div by 2&3&5-16
  div by2&3&7-111
  div by3&5&7-4
  div by2&5&7-7
  total-38
  and
  div by 2&3&5&7- 2
  So sol is 587-224+38-2=385
  
• 8 years agoHelpfull: Yes(0) No(0)