# In order to protect from COVID 19 the head of a residential colony orders 960 hand gloves 3360 face mask and 1440 hand sanitizers. Assume that each family of the colony get the same number of hand gloves, face masks and hand sanitizers. Find the maximum number of families possible, in that community.

$\begin{array}{l}\text{Total hand gloves}=960\\ \text{Face masks}=3360\\ \text{Hand sanitizers}=1440\\ \text{given that each family will get same number of items listed above.}\\ \text{Maximum number of families}=?\\ \text{To get}\ \text{maximum number of families}\ \text{we need to find out H.C.F of }960,3360\text{ and }1440\\ \text{Factors of }\ 960=2\times2\times2\times2\times2\times2\times3\times5\times1\\ \text{Factors of }3360=2\times2\times2\times2\times2\times3\times5\times7\times1\\ \text{Factors of }1440=2\times2\times2\times2\times2\times2\times5\times3\times3\times1\\ \text{H.C.F}=2\times2\times2\times2\times2\times3\times5\times1=480\\ \text{Maximum number of families}=\text{H.C.F}=480.\\ \end{array}$

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