Question

215 crayons, 65 pencils, and 40 paint brushes are to be packed in stationery boxes such that each box has only one kind of item and the number of items in each box is the same.
What is the greatest number of items each box can have?

• A. 5
• B. 20
• C. 15
• D. None of the above

Answer 1

The correct option is A 5

To solve this problem, first we have to break down the numbers into prime factors.

The prime factorization of 215 is: 5 × 43
The prime factorization of 65 is: 5 × 13
The prime factorization of 40 is: 2 × 2 × 2 × 5

Thus, the greatest common divisor is 5.

Hence, there can be a maximum of 5 items in each box.

Additionally,
Number of boxes with crayons: 215 ÷ 5 = 43
Number of boxes with pencils: 65 ÷ 5 = 13
Number of boxes with paint brushes: 40 ÷ 5 = 8