Question

Eva has a total of 6 candies. She wants to arrange them in rows, each with the same number of candies. How many different ways she could arrange the candies to make a perfect rectangle?

• A. 4
• B. 5
• C. 3
• D. 2

Answer 1

Answer: (A)

4
Total candies she has: 6
Factors of 6 are 1, 2, 3, 6
Let denotes a candies

Case 1: C
C
C
C
C
C
Total rows = 6
Total Columns = 1
Dimensions of rectangle = Total rows x Total columns
= 6$\times$1 = 6

Case 2: C C
C C
C C
Total rows = 3
Total Columns = 2
Dimensions of rectangle = Total rows x Total columns
= 3$\times$2 = 6

Case 3: C C C
C C C
Total rows = 2
Total Columns = 3
Dimensions of rectangle = Total rows x Total columns
= 2$\times$3 = 6

Case 4: C C C C C C
Total rows = 1
Total Columns = 6
Dimensions of rectangle = Total rows x Total columns
= 1$\times$6 = 6

$\therefore$ There are 4 ways to arrange 4 candies into the perfect rectangle