There are 312, 260 and 156 students in class 6,7 and 8 respectively. Buses are to be hired to take these students to a picnic. Find the maximum number of students who can sit in a bus if each bus takes equal number of students. Find also the number of buses required.

Given :

There are 312, 260 and 156 students in class 6,7 and 8 respectively.

To find :

We have to find the maximum number of students who can sit in a bus if each bus takes equal number of students.

Solution :

We have to find the HCF of the students.

HCF of 312,260 and 156 is,

$312 = 2 \times 2 \times 2 \times 3 \times 13$

$260 = 2\times2\times5 \times13$

$156 = 2\times2\times2\times13$

$HCF = 2 \times2 \times13 = 52$

Therefore,

The maximum number of students who can sit in a bus if each bus takes equal number of students is 52.

$Number of buses required = \frac{Total number of students}{Number of students in a bus}$

                                                 $=\frac{ (312+260+156)}{52}$

                                                 $= \frac{728}{52}$

                                                 $= 14$.

Maximum number of students can sit in a bus is 52.

Number of buses required is 14.

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Updated on: 10-Oct-2022

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