~~. Find the greatest number which will divide 264 and 168 exactly leaving a remainder of 8 in each case

Given numbers : 264 and 168

On dividing these given numbers by the greatest number, we get same remainder 8.

From the given numbers, we now subtract the remainder 8

264 - 8 = 256

 168 - 8 = 160  

Now, we will take the H.C.F of  256 and 160.

$$\begin{gathered} \mathrm{Prime} \mathrm{factorisation} \mathrm{of} 256 \mathrm{and} 160 \mathrm{is} : \\ 256 = 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2 \\ 160 = 2\times 2\times 2\times 2\times 2\times 5 \\ \mathrm{HCF} = 2\times 2\times 2\times 2\times 2= 32 \end{gathered}$$
Therefore, 32 is the greatest number required.