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?
Accepted Solution
A:
Answer:8 boxesStep-by-step explanation:To solve this question you must find the prime factors of both numbersApples number: 64 Oranges number: 24Then:64| 232| 2 16| 28 | 24 | 22 | 21 [tex]64=2^6[/tex]24| 212| 26 | 23 | 31[tex]24=2^3 * 3[/tex]Now we take the common factors in both terms with their lowest exponent.2 is a common factor and its smallest exponent is 3: [tex]2^3=8[/tex]So the largest number of boxes you can make is 8The number of apples that each box contains is:[tex]apples = \frac{64}{8}=8[/tex]The number of oranges that each box contains is:[tex]oranges = \frac{24}{8}=3[/tex]