How do I solve this ?

Answer= 24

first of all separate it into 2 different fractions. 583*584*585*586*587*588/720. cancel the numerator and denominator using 20. then it the remainder will be 3*4*5*6*7*8/36. but by remainder theorem we have divided numerator and denominator with 20 so the actual remainder will 36 time the remainder obtained.so the actual remainder we get is (3*4*5*6*7*8)*36. So the remainder will be further reduced to 0.  then the second fraction remains. but remainder theorem its remainder is -1*-2*-3*-4=24