What is the largest number that on diving 729 and 901 leaves remainder 9 and 5 respectively?

1. The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively, is

We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r). Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896

Hence , required answer = 16.