A wholesale tea dealer has 408 kilograms,468 | vedclass

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(D) To find the capacity of the largest possible box that can pack each quantity of tea completely,we need to calculate the Highest Common Factor $(H.

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(D) To find the capacity of the largest possible box that can pack each quantity of tea completely,we need to calculate the Highest Common Factor $(H.C.F.)$ of $408, 468,$ and $516$.Step $1$: Prime factorization of $408 = 2^3 	imes 3 	imes 17$.Step $2$: Prime factorization of $468 = 2^2 	imes 3^2 	imes 13$.Step $3$: Prime factorization of $516 = 2^2 	imes 3 	imes 43$.Step $4$: The $H.C.F.$ is the product of the lowest powers of common prime factors,which is $2^2 	imes 3 = 4 	imes 3 = 12$.Therefore,the capacity of the largest possible box is $12 	ext{ kg}$.

$A$ wholesale tea dealer has $408$ kilograms,$468$ kilograms,and $516$ kilograms of three different qualities of tea. He wants to pack all of it into boxes of equal size without mixing the different qualities. Find the capacity of the largest possible box.

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