Total no. of students in the 3 classes : 312 + 260 + 156
= 728
Prime factorisation of 728 = 2 x 2 x 2 x 7 x 13
To have the maximum no. of students in a single bus, we must have the minimum no. of buses possible.
We can see that 2 is the smallest number in the prime factorisation, so if we assume that 2 buses will be hired to take the students to the picnic, the maximum no. of students in a bus can be:
(2 x 2 x 2 x 7 x 13 ) / 2
= 2 x 2 x 7 x 13
= 364
Therefore, the maximum no. of students who can sit in a single bus is 364. (The bus has to be very huge!)
Hope this helps!
