Aschool is preparing fruit baskets for a local nursing home. there are 162 apples, 108 oranges, and 180 bananas. if the baskets are identical and there is no leftover fruit, what is the greatest number of baskets that can be made? how many apples, oranges, and bananas are in each basket?

To solve this exercise, we must calculate the Maximum Common Divisor (M.C.D.), which is the greatest common divisor of 62,108 and 180. We apply factor decomposition, and we obtain:

 162= (3^4)(2)

 108= (2^2)(3^3)

 180= (2^2)(3^2)(5)

 We choose the common numbers with their lowest exponent:

 M.C.D.= (2)(3^2)

 M.C.D.= 2x9

 M.C.D.= 18

 The greatest number of baskets that can be made is: 18 baskets

 To know how many apples, oranges and bananas are in each basket, we must divide the greatest number of them that can be made between the total amount of apples, oranges and bananas, as shown below:

 162/18= 9 apples

 108/18= 6 oranges

 180/18= 10 bananas

 So, there are 9 apples, 6 oranges and 10 bananas in each basket.

answer: the equation matches the regression

step-by-step explanation: