How many positive integers N are there such that LCM of N and 1000 is 1000

• 1000=2^3*5^3
  no. of factors of 1000=(3+1)*(3+1)=16
  LCM of each factor of 1000 & 1000 will be 1000
  so N=16
• 10 years agoHelpfull: Yes(3) No(0)
• 15
  All the positive factors will share 1000 as a LCM with them and 1000.
  Factors are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500 Total=15
• 10 years agoHelpfull: Yes(1) No(0)
• 1*1000;
  2*500;
  4*250;
  5*200;
  8*125;
  10*100;
  20*50;
  25*40;
  so totally 16 possiblities
  and atlast 1000,1000
  so a total of 17.
• 10 years agoHelpfull: Yes(0) No(2)