The HCF of three natural nos x,y,z is 13. if the sum of x,y,z is 117 then how many ordered pairs of (x,y,z) exist?

1) 27
2) 54
3) 28
4) 55

• number are x=13a,y=13b,z=13c where a,b,c not equal to 0
  x+y+z=117
  a+b+c=9
  the numbers are a=1,b=1,c=7 = 3
  the numbers are a=1,b=2,c=6 = 3!=6
  the numbers are a=1,b=3,c=5 = 3!=6
  the numbers are a=1,b=4,c=4 = 3
  the numbers are a=2,b=2,c=5 = 3
  the numbers are a=2,b=3,c=4 = 3!=6
  the numbers are a=3,b=3,c=3 = 1
  ordered pairs are = 3+6+6+3+3+6+1=28 (3) answer
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