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.

Answer 1

The number of rooms will be minimum if each room accommodates a maximum number of teachers. Since in each room the same number of teachers are to be seated and all of them must be of the same subject. Therefore, the number of teachers in each room must be HCF of 48, 80, and 144.

The prime factorisations of 48, 80 and 144 are as under 

48 = 2⁴ × 3¹

80 = 2⁴ × 5¹

144 = 2⁴ × 3²

∴ HCF of 48, 80 and 144 is 2⁴ = 16

Therefore, in each room 16 teachers can be seated.

∴ No. of room required = ${\displaystyle \frac{\text{Total no. of teachers}}{16}}$

= ${\displaystyle \frac{48+80+144}{16}}$

= ${\displaystyle \frac{272}{16}}$

= 17