In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively. Find the minimum number of rooms required if in each room the same number of teacher

Question

In a teachers' workshop, the number of teachers teaching French, Hindi and English are 48, 80 and 144 respectively. Find the minimum number of rooms required if in each room the same number of teachers are seated and all of them are of the same subject.

Accepted Answer

Step 1: Minimum number of rooms required means there should be maximum number of teachers in a room. We have to find HCF of 48, 80 and 144.
Step 2: $48 = 2^4 	imes 3$
$80 = 2^4 	imes 5$
$144 = 2^4 	imes 3^2$
Step 3: HCF $(48, 80, 144) = 2^4 = 16$
Total number of rooms required $= \frac{48}{16} + \frac{80}{16} + \frac{144}{16} = 3 + 5 + 9 = 17$

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