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Question
Alex has 12 party hats and 14 balloons. He wants to put the same number of items of one type in each goodie bag. What is the greatest number of party hats or balloons he can put in each goodie bag?
Alex has 12 party hats and 14 balloons. He wants to put the same number of items of one type in each goodie bag. What is the greatest number of party hats or balloons he can put in each goodie bag?
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Solution
The correct option is A 2
To solve this problem, first we have to break down both the numbers into prime factors.
The prime factorization of 12 is: 2 × 2 × 3
The prime factorization of 14 is: 2 × 7
Thus, the greatest common divisor of 12 and 14 is 2.
Hence, he can have 2 items in each goodie bag, i.e., either 2 party hats or 2 balloons.
Additionally,
Number of bags of party hats = 12 ÷ 2 = 6
Number of bags of balloons = 14 ÷ 2 = 7
To solve this problem, first we have to break down both the numbers into prime factors.
The prime factorization of 12 is: 2 × 2 × 3
The prime factorization of 14 is: 2 × 7
Thus, the greatest common divisor of 12 and 14 is 2.
Hence, he can have 2 items in each goodie bag, i.e., either 2 party hats or 2 balloons.
Additionally,
Number of bags of party hats = 12 ÷ 2 = 6
Number of bags of balloons = 14 ÷ 2 = 7
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