How many positive integers N are there such that the least common multiple of N and 1000 is 1000?

• 1000=2^3*5^3
  total no. of factors of 1000= (3+1)*(3+1)=16
  LCM of each factor of 1000 & 1000 will be 1000
  
  no. of positive integers = 16
• 10 years agoHelpfull: Yes(42) No(0)
• 1000=2^3 * 5^3
  number of factors of 1000= 4*4= 16
  
• 10 years agoHelpfull: Yes(6) No(0)
• 16
  LCM(N;1000)=1000 then N must be a divisor of 1000
  1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 80, 100, 125, 250, 500, 1000
• 10 years agoHelpfull: Yes(5) No(5)
• 1000=2^3*5^3
  No of factors= (power of 2 + 1)*(power of 5 + 1)=(3+1)(3+1)=16
  (This formula is not working for 1 coz 1 has only one factor i.e. 1)
• 10 years agoHelpfull: Yes(3) No(0)
• ans should be 15
  16-1=15 N != 1000
  
• 10 years agoHelpfull: Yes(0) No(0)
• 16 is the correct answer
• 8 years agoHelpfull: Yes(0) No(0)