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Ella is building fruit baskets and is filling them with apples and oranges. She has 48 apples and 60 oranges, and wants to make sure each each fruit basket has the same number of apples and oranges with no fruit left over. Choose all options that can be used to make fruit baskets? Select all that apply.

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Answer:

Ella could make:

2, 3, 4, 6, or 12 fruit baskets.

Step-by-step explanation:

We know that Ella has 48 apples and 60 oranges.

She wants to make N fruit baskets, such that each one of these fruit baskets has the same number of each fruit.

So we can define the variables:

a = number of apples in each one of these baskets

o = number of oranges in each one of these baskets

Then, if we have N baskets, we must have that:

N*a = 48

N*o = 60

a = 48/N

o = 60/N

And the values of a and o must be integers, then N must be a common factor of 48 and 60.

Remember that every number can be written as a product of prime factors, then let's rewrite 48 and 60 in that way:

48 = 2*24 = 2*2*12 = 2*2*2*2*3

60 = 2*30 = 2*3*10 = 2*2*3*5

Then, the common factors between 48 and 60 are the ones we can make with the prime numbers (that appear in both constructions) these are:

2

3

2*2 = 4

2*3 = 6

2*2*3 = 12

These are all the possible numbers of fruit baskets.

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