sheila has to make gift hampers out of 40 bananas, 24 oranges and 16 pineapples .the gift hampers have to be identical and contain at least one type of fruit. what is the maximum number of such gift hampers that she can make without leaving any fruit?

Answer :

Given  :  Sheila has to make gift hampers out of 40 bananas, 24 oranges and 16 pineapples . 
So,
To find maximum number of gift hampers that she can make without leaving any fruit , Where the gift hampers have to be identical and contain at least one type of fruit.
We find HCF of 40   ,  24 and 16  and get

40 =  2 $\times$ 2 $\times$ 2 $\times$ 5 

24  =  2 $\times$ 2 $\times$ $\times$ 2 $\times$ 3

16 =  2 $\times$ 2 $\times$ 2 $\times$ 2 
So,
HCF (  40 , 24 and 16 ) =  2 $\times$ 2 $\times$ 2  =   8 
So,
Maximum number of gift hampers that she can make without leaving any fruit  = $\frac{40 + 24 + 16}{8} = \frac{80}{8} = \mathbf{10}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathit{A}\mathit{n}\mathit{s}\mathbf{ }\mathbf{)}$