You are making fruit baskets using 54 apples, 36 oranges and 73 bananas. What is the greatest number of identical baskets you can make? Why can’t you use all of the fruit?

73 has no factors other than 1 and 73.

You cannot make 1 basket with no leftovers, since there are not 73 od the other fruits.
Similarly, you cannot make 73 baskets with one of each fruit.
So, no matter how many baskets you make with the same number of apples and oranges, there will be bananas left over.
GCF(54,36) = 18
So, you can make 18 baskets with 3 apples and 2 oranges and 3 bananas.

54 = 6*9 = 2*3*3*3

36 = 4*9 = 2*2*3*3
73 > 8*9 by 1
So making 9 baskets will leave us with only 1 fruit left over
(each basket will contain: 6 apples, 4 oranges and 8 bananas, with 1 banana left over)

Answering the question verbatim, we could make a maximum of 36 baskets
with one of each of the fruit, but that means we would have 53 apples,
35 oranges, and 72 bananas left over. I don't think that is what you had in mind.
I assumed you wanted the least amount of fruit left over.

I messed up

Go with oobleck, I missed the part where 2 is still a common factor

Each of my 9 baskets of 6 apples, 4 oranges and 8 bananas
can be divided in half, so 18 baskets of 3 apples, 2 oranges, and 4 bananas, with
1 banana left over.

dang! Nice catch on the banana count, Reiny!

good job guys

Well, let me calculate that for you.

First, let's find the greatest common divisor (GCD) between the numbers of apples, oranges, and bananas. The GCD of 54, 36, and 73 is 1.

So, since the GCD is 1, it means there are no common factors between the three numbers. Therefore, you can't make any identical baskets using all of the fruit, unfortunately.

But don't be too sad, you can always create some unique and eclectic fruit baskets! Who wants identical when you can have variety, right?

Deez