The $H.C.F.$ and $L.C.M.$ of two numbers are $8$ and $48,$ respectively. If one of the numbers is $24,$ then the other number is

Find the greatest number of five digits which when divided by $4, 6, 10$ and $15$ leaves the same remainder $3$ in each case.

The greatest number that divides $411, 684,$ and $821$ and leaves $3, 4,$ and $5$ as remainders,respectively,is

The fraction $\frac{1095}{1168}$ when expressed in its simplest form is:

Find the least number which when divided by $16, 18, 20$ and $25$ leaves $4$ as a remainder in each case,but when divided by $7$ leaves no remainder.

Find the largest number of four digits exactly divisible by $14, 24, 27$ and $32$.