Question

a farmer is putting apples and oranges into boxes to sell at a market. he has 64 apples and 24 oranges. what is the greatest number of boxes he can make using all of the apples and oranges if each box has identical contents?​

Answer 1

8 boxes.

Explanation:

We have been given that a farmer is putting apples and oranges into boxes to sell at a market. He has 64 apples and 24 oranges.

To find the greatest number of boxes he can make using all of the apples and oranges, we need to find Greatest Common Factor of 64 and 24.

Factors of 64: 1, 2, 4, 8, 8, 16, 32, 64.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.

We can see that greatest common factor of 64 and 24 is 8, therefore, the farmer can make 8 boxes using all of the apples and oranges.

Answer 2

8 boxes

Explanation:

To solve this question you must find the prime factors of both numbers

Apples number: 64

Oranges number: 24

Then:

64| 2

32| 2

16| 2

8 | 2

4 | 2

2 | 2

1

`64=2^6`

24| 2

12| 2

6 | 2

3 | 3

1

`24=2^3 * 3`

Now we take the common factors in both terms with their lowest exponent.

2 is a common factor and its smallest exponent is 3:
`2^3=8`

So the largest number of boxes you can make is 8

The number of apples that each box contains is:

`apples = (64)/(8)=8`

The number of oranges that each box contains is:

`oranges = (24)/(8)=3`