Question

$600$ males and $492$ females need to be transported from an island via sea. Find the maximum number of trips required if number of males and number of females in each trip remains constant.

• A. $6$
• B. $4$
• C. $10$
• D. $12$

Answer 1

The correct option is D $12$

For maximum number of trips of the vessel, each trip should consist of minimum number of passengers, given that number of males and number of females in each trip remains constant.

$\therefore$ We need to find the greatest common divisor of $600$ and $492.$

Using prime factorization,
$600=6\times 100=2\times 3\times 2\times 2\times 5\times 5$
$=2^3\times 3\times 5^2$

$492=2\times 2\times 3\times 41$
$=2^2\times 3\times 41$

$\therefore$ The common factors are $2,3,4,6\&12$.
Hence, Greatest common factor or GCD is 12.

The maximum number of trips required is $12.$