**Q) 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.**

**Ans:**

**STEP BY STEP SOLUTION**

The number of rooms will be minimum if number of participant in each room are maximum.

Since all participant in a room have to be of same subject, we need to take HCF of all three numbers.

By prime factorisation,

48 = 2 x 2 x 2 x 2 x 3

80 = 2 x 2 x 2 x 2 x 5

144 = 2 x 2 x 2 x 2 x 3 x 3

∴ HCF of 48, 80, 144 = 2 x 2 x 2 x 2 = 16

Number of rooms required = Rooms required for French teachers + Rooms required for Hindi teachers + Rooms required for English teachers

=

= 3 + 5 + 9 = 17

**Therefore, minimum 17 rooms are required.**

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