1000 = 2^3 * 5^
When we say HCF of factors (x,y,z) = 1 ; then we mostly talk of 3 cases ..
Case -1 ; ( 1, 2^3, 5^3) ..now here ordered arrangements = 3^2*3! = 54
Case - 2 ( 1, 1, 2^3) ; (1, 1, 5^3) ; (1, 1, 2^3 * 5^3)now total arrangement of these cases is 3!/2! ( 15) = 45
case -3 when (1 , 1, 1) ; as we are taking of factors of 1000 with HCF 1 , so this has to be a case ... And it can be arranged in only n only 1 way .. so 1
So finally 54 + 45 + 1 = 100