Question

Britney is a costume designer. She had $52$ circular buttons, $56$ square buttons, and $60$ rectangular buttons for designing purposes. How many maximum dresses can she design so that no buttons are left? Also, find the number of square buttons that are used in each dress?

• A. She can make total $4$ dresses.
• B. $14$ square bottons will be used in each dress.
• C. She can make total $6$ dresses.
• D. $13$ square bottons will be used in each dress.

Answer 1

Answer: (A), (B)

$14$ square bottons will be used in each dress.

Number of circular buttons $=52$
Number of square buttons $=56$
Number of rectangular buttons $=60$

As each dress has the same combinations of buttons, the number of each botton type in each dress should be a common factor of the total number of bottons of each kind.

The maximum number of dresses she can make will be the GCD of each type of button, i.e., $52,56$ and $60$.




$52=2\times 2\times 13$
$56=2\times 2\times 2\times 7$
$60=2\times 2\times 3\times 5$
GCD is $2\times 2=4$.
So, she can make $4$ dresses.

Number of square buttons used in each dress $=\frac{\text{Total number of square bottons}}{\text{Total number of dresses}}=\frac{56}{4}=14$.