Jenny is making fruit baskets. She has 12 apples, 30 pears, and 42 oranges. Each basket has the same number of pieces of each type of fruit. What is...

We are given
that Jenny has 12 apples, 30 pears, and 42 oranges. If she is making fruit baskets, each of
which contain the same number of each fruit, what is the largest number of baskets that she can
make?

(Each basket must contain the same number of apples, but the number of
apples and pears can be different.)

To try to use a brute-force method, we
would have to be very organized, as there are three types of fruit. The efficient method is to
realize that we need the greatest common factor (also called the greatest common divisor) of 12,
30, and 42. This is due to the fact that the number of each type of fruit must be the same so
only factors of the amounts of fruit will work. We need a common factor as this will yield the
same number of baskets:

12: 2*2*3
30: 2*3*5
42:
2*3*7

To find the greatest common factor we take each factor that appears in
all three lists to the lowest power.

GCF(12,30,42)=2*3=6

Thus 6 is the number of baskets. Each basket will contain 2 apples, 5
pears, and 7 oranges.

Examples of similar problems
include:

1) If you're distributing 26 pens and 39 pencils to students, and
each student receives the same number of each, what is the maximum number of students? (Or you
could distribute 9 binders, 21 packs of paper and 51 dividers, etc.)

2) There
are 15 girls and 12 boys in a class. What is the greatest number of rows you can have if each
row has the same number of girls and and the same number of boys?

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