The greatest number, which when divided by 989 and 1327 leaves remainders 5 and 7 respectively is

1. The greatest number, which when divide 989 and 1327 leave remainders 5 and 7 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 (989 – 5) and (1327 – 7)Required number = HCF of 984 and 1320 = 24

∴ HCF = 24