1. Three sets of English, Hindi, and Urdu books are to be stacked in such a way
that the books are stored subject wise and the height of each stack is the same.
The numbers of English, Hindi and Urdu books are 336, 192 and 144 respectively.
Assuring that the books have that same thickness, determine the number of
stacks of English, Hindi and Urdu books.

To ensure the stacks are of equal height, we need to find a common divisor of the total number of books in each language. We’ll use the greatest common divisor (GCD) of the numbers of books to determine this common height.

Calculate the GCD of 336, 192, and 144:

First, find the prime factorizations:

336=2²×2²×3×7

192=2³×2³×3

144=2²×2²×3²

The GCD is found by taking the lowest power of each common prime factor:

For

2 The minimum power is 2²×2²

For3 The minimum power is 3

Thus, the GCD is:GCD=2²×2²×3=16×3=48

Determine the number of stacks for each language:

English Books: 336/48 =7 stacks

Hindi Books:192/48=4 stacks

Urdu Books: 144/48 =3 stacks

Therefore, the number of stacks of English books is 7, Hindi books is 4, and Urdu books is 3.