Question

A car dealer has $72$ BMW and $64$ Mercedes in his showroom. The dealer wants to arrange the cars in rows so that each row has the same number of vehicles of each type. What is the greatest possible number of rows that can be formed?

• A. $18$
• B. $6$
• C. $8$
• D. $24$

Answer 1

The correct option is C $8$

Number of BMW $=72$
Number of Mercedes $=64$
Greatest number of rows will be GCD of number of vehicles of each type, i.e. GCD of $72$ and $64.$


$72=2\times 2\times 2\times 3\times 3$
$64=2\times 2\times 2\times 2\times 2\times 2$
GCD is $2\times 2\times 2=8$

$\therefore$ Required number of rows is $8.$
Here, we will have 9 BMW and 8 Mercedes in each row.