Question

Find the smallest number by which 1944 should be divided, so that the quotient is a perfect square.

• A. 2
• B. 3
• C. 6
• D. 12

Answer 1

The correct option is C 6

$1944=2\times 2\times 2\times 3\times 3\times 3\times 3\times 3$
Since, the prime factors 2 and 3 cannot be paired.
$\therefore$ The given number should be divided by $2\times 3=6$
$\frac{1944}{6}=\frac{2\times 2\times 2\times 3\times 3\times 3\times 3\times 3}{2\times 3}$
$=2\times 2\times 3\times 3\times 3\times 3=324={18}^2$