There are $477,371$ and $424$ students in three different classes of a vidyalaya going to a hill station for a picnic. Buses are to be hired to take students to the picnic site. Find the maximum number of students who can sit in a bus, if each bus carries equal number of students. Also, find the number of buses required for this purpose.

Let x be the HCF of number of students who can sit in a bus.

To find the HCF of number of students.

Prime factorisation of $477=3^2\times 53$

Prime factorisation of $371=7\times 53$

Prime factorisation of $424=2^3\times 53$

$\mathrm{HCF}\mathrm{of}(477,371,424)=53$

Therefore, the number of students who can sit in each bus is $53$.

Calculate the required no of buses.

$\begin{array}{rcl}\mathrm{Required}\mathrm{number}\mathrm{of}\mathrm{buses}& =& \frac{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{students}}{\mathrm{No}.\mathrm{of}\mathrm{students}\mathrm{in}\mathrm{each}\mathrm{bus}}\\ & =& \frac{477+371+424}{53}\\ & =& \frac{1272}{53}\\ & =& 24\end{array}$

Hence, the required number of buses is $24$.