The $HCF$ of $x^{8}-1$ and $x^{4}+2x^{3}-2x-1$ is

Find the greatest number of four digits which must be added to $5231$ so that the final number becomes exactly divisible by $12, 15, 27, 32$ and $40$.

Find the maximum possible length which can be used to measure exactly the lengths $6 \, m$,$4 \, m \, 75 \, cm$,and $10 \, m \, 25 \, cm$. (in $, cm$)

What is the least number of cut pieces of equal length that can be cut out of two lengths $10\, m\, 857\, mm$ and $15\, m\, 87\, mm$?

$A$ wholesale tea dealer has $408$ kilograms,$468$ kilograms,and $516$ kilograms of three different qualities of tea. He wants to pack all of it into boxes of equal size without mixing the different qualities. Find the capacity of the largest possible box.

The least number which when divided by $5, 6, 7$ and $8$ leaves $3$ as a remainder,but when divided by $9$ leaves no remainder,is: