In a seminar, the number of participants in  English , Maths  and Science are 175, 140 and 105 respectively. Find the minimum number of rooms required if in each room the same number of participants of the same subject are to be accomodated

Solution:-
In this question we need to find the minimum number of rooms which can happen if each room accommodates maximum number of participants and  in each room the same number of participants has  to be seated and all of them must has the same subject. Therefore, the number of participants in each room must be equal to the HCF of 175, 140 and 105.
 Now, HCF by prime factorization 
175=5*5*7
140=2*2*5*7
105=3*5*7
Hence, HCF=5*7=35
                   
 Therefore, in each room 35 participants can be seated.
So, number of rooms required = Total number of participants/ 35 = (175 + 140+ 105) / 35 = 12

 

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