Sol.
Q.
There are 156, 208 and 260 student in Groups A , B and C respectively. Buses are to be hired to take them for a field trip. Find minimum number of buses to be hired if the same number of students be accommodated in each bus.
The number of Buses will be minimum if each bus accommodated maximum number of students.
∴
The no. of students in each bus must be HCF of 156, 208 and 260 students.
The prime factorisation of 156 , 208 and 260 are :
156
156
78
39
2
2
3
13
13
1
=
×
3
×
13
22
208
104
52
2
2
2
26
2
13
13
1
208
=
×
13
24
260
130
65
2
2
5
13
13
1
260
=
×
5
×
13
22
∴
HCF of 156, 208 and 260
=
×
13
22
=
52
∴
In each bus 52 students can be accommodated
=
∴ Minimum no. of buses required
Total no. of students
52
=
156 + 208 + 260
52
=
624
52
=
18 buses.
∴
18 no. of buses will be hired if the same number of students be accommodated in each bus.