What is the smallest number by which 5600 mus | vedclass

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(D) To find the smallest number by which $5600$ must be divided to make it a perfect cube,we first find the prime factorization of $5600$.$5600 = 56 \

Vedclass · Accepted Answer

$700$

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(D) To find the smallest number by which $5600$ must be divided to make it a perfect cube,we first find the prime factorization of $5600$.$5600 = 56 	imes 100 = (8 	imes 7) 	imes (10 	imes 10) = (2^3 	imes 7) 	imes (2 	imes 5 	imes 2 	imes 5) = 2^3 	imes 7 	imes 2^2 	imes 5^2 = 2^5 	imes 5^2 	imes 7^1$.For a number to be a perfect cube,the exponent of each prime factor in its prime factorization must be a multiple of $3$.In $2^5 	imes 5^2 	imes 7^1$,the exponents are $5, 2,$ and $1$.To make these exponents multiples of $3$ by division,we need to remove the factors that prevent this:- For $2^5$,we divide by $2^2$ to get $2^3$.- For $5^2$,we divide by $5^2$ to get $5^0 = 1$.- For $7^1$,we divide by $7^1$ to get $7^0 = 1$.Therefore,the number to be divided is $2^2 	imes 5^2 	imes 7^1 = 4 	imes 25 	imes 7 = 100 	imes 7 = 700$.

What is the smallest number by which $5600$ must be divided to make it a perfect cube?

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