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Question
Anza bakes 30 pumpkin pies and 48 apple pies. She wants to divide the pies into identical boxes such that each box has only one kind of pie.
What is the maximum number of pies each box can have?
Anza bakes 30 pumpkin pies and 48 apple pies. She wants to divide the pies into identical boxes such that each box has only one kind of pie.
What is the maximum number of pies each box can have?
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Solution
The correct option is A 6
To solve this problem, first we have to break down both the numbers into prime factors.
The prime factorization of 30 is: 2 × 3 × 5
The prime factorization of 48 is: 2 × 2 × 2 × 2 × 3
Thus, the greatest common divisor of 30 and 48 is 2 × 3 = 6
Hence, each box will have 6 pies.
Additionally,
Number of boxes with pumpkin pies: 30 ÷ 6 = 5
Number of boxes with apple pies: 48 ÷ 6 = 8
To solve this problem, first we have to break down both the numbers into prime factors.
The prime factorization of 30 is: 2 × 3 × 5
The prime factorization of 48 is: 2 × 2 × 2 × 2 × 3
Thus, the greatest common divisor of 30 and 48 is 2 × 3 = 6
Hence, each box will have 6 pies.
Additionally,
Number of boxes with pumpkin pies: 30 ÷ 6 = 5
Number of boxes with apple pies: 48 ÷ 6 = 8
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