Question

Visualizing Euclid’s division algorithm, find the values of $a,b$ and $c.$

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

Answer 1

The correct option is B

$a=12,b=12,c=3$

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 $c=3.$