In a seminar, the number of participants in subjects A, B and C are 96, 160 and 224, respectively. Find the minimum number of rooms required if in each room the same number of participants are seated and all participants in a room are from the same subject.

Correct option is D

Given:

Number of students in subjects A, B and C = 96,160 and 224 respectively

Formula Used:

HCF is the highest common number which divides the numbers without leaving any remainder

Solution:

To find the number of students in each class such that in particular class students are of same subjects we have to find the HCF

Prime Factorization of 96,160 and 224 is:

96 =$$2^5 \times 3$$​​

160 =$$2^5 \times 5$$​​

224 =$$2^5 \times 7$$​​

HCF =$$2^5 = 32$$​​

Hence there are 32 students in each class

Total number of class required:

Total number of students = 96+160+224 = 480

Number of classes required =$$\frac{480}{32}$$​= 15