Find the two largest numbers of four digits having $531$ as their $H.C.F$.

Three pieces of timber $42 \ m$,$49 \ m$,and $63 \ m$ long have to be divided into planks of the same length. What is the greatest possible length of each plank (in $m$)?

In a school,$391$ boys and $323$ girls have been divided into the largest possible equal classes,so that each class of boys numbers the same as each class of girls. What is the number of classes?

Find the least number which when divided by $2, 3, 4, 5$ and $6$ leaves $1, 2, 3, 4$ and $5$ as remainders,respectively,but when divided by $7$ leaves no remainder.

The $L.C.M.$ and $G.C.D.$ of two numbers are $1530$ and $51,$ respectively. Find how many such pairs are possible?

What is the least number which,when divided by $5, 6, 7, 8$ gives the remainder $3$ but is divisible by $9$?