How many of the first 2100 natural numbers are either prime to 6,15 or 35 ?

1) 700
2) 400
3) 520
4) 640

• It can be done with the help of co-prime theorem.
  co-prime of 6=(2100)(1-1/2)(1-1/3)=700
  co-prime of 15=2100(1-1/3)(1-1/5)=1120
  co-prime of 35=2100(1-1/5)(1-1/7)=1440
  
  Now you have to extract the numbers which are prime to both 6 and 15,both 15 and 35 and both 6 and 35.
  
  co-prime to both 6 and 35 is with the same logic.
  2100(1-1/2)(1-1/3)(1-1/5)(1-1/7)=480
  and common for both 6 and 15,
  2100(1-1/3)(1-1/5)(1-1/2)=560
  and common for both 15 and 35,
  2100(1-1/3)(1-1/5)(1-1/7)=960
  
  actually to find the exclusive prime number we have to extracts the prime numbers that cross off the summations of co primes.
  
  So the answer is=(700+1120+1440)-2((560-480)+(960-480))-3*480=700.
• 11 years agoHelpfull: Yes(0) No(1)