Blake puts apples and pears into boxes for the customers at the local food bank. He puts the same number of apples or pears in each box. Each box has only one type of fruit There are 64 apples and 48 pears. What is the largest number of pieces of fruit Franklin can put in a box?

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Eudoraid Eudoraid · Answer 1

To solve this problem, find the greatest common factor of the numbers representing the numbers of apples and pears respectively.

Each box will contain 3 pears and 4 apples.

And total number of fruits in each box will be 7 fruits.

It's given in the question,

To find the greatest number of fruits he can put in a box we will find the greatest common factor (GCF) of the given numbers first.

[tex]48=1\times 2\times 2\times 2\times 2\times 3[/tex]

[tex]64=1\times 2\times 2\times 2\times2 \times2\times 2[/tex]

Therefore, greatest common factor of these numbers = [tex]1\times 2^{4}[/tex] = [tex]16[/tex]

GCF of these numbers tells about the number of boxes that can be prepared.

Now the number of pears that can be put in each box = [tex]\frac{48}{16}=3[/tex]

And the number of apples in each box = [tex]\frac{64}{16}=4[/tex]

Therefore, each box will contain 3 pears and 4 apples.

And total number of fruits in each box = 3 + 4 = 7 fruits.

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