Question

Visualizing Euclid’s division algorithm, is the values of \(a, b\) and \(c.\)
15 27

• A. a = 11, b =8, c =4
• B. a = 10, b =12, c =5
• C. a = 12, b =12, c =3
• D. a = 13, b =11, c =2

Answer 1

The correct option is C a = 12, b =12, c =3

The image visualises Euclid’s division algorithm for 27 and 15.

$27=15\times 1+12$
The divisor (15) of this first step becomes the dividend of next step and the remainder(12) of the first step becomes the divisor of the next step.

$\Rightarrow 15=12\times 1+3$
The divisor (12) of this first step becomes the dividend of next step and the remainder(3) of the first step becomes the divisor of the next step.

$12=3\times 4+0$
Since the remainder is zero, the HCF of 27 and 15 is 3 using Euclid’s division algorithm.

Thus, the side length of the smallest square in the figure is 3.
$⟹c=3$
$⟹b=4\times 3=12$
So, the answer will be $a=12,b=12$ and $c=3.$