The smallest number by which 3600 must be mul | vedclass

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Question

(B) First,find the prime factorization of $3600$: $3600 = 2 	imes 1800 = 2^2 	imes 900 = 2^3 	imes 450 = 2^4 	imes 225 = 2^4 	imes 3^2 	imes 5^2

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(B) First,find the prime factorization of $3600$: $3600 = 2 	imes 1800 = 2^2 	imes 900 = 2^3 	imes 450 = 2^4 	imes 225 = 2^4 	imes 3^2 	imes 5^2$. To make a number a perfect cube,the exponent of each prime factor in its prime factorization must be a multiple of $3$. In $3600 = 2^4 	imes 3^2 	imes 5^2$,the exponents are $4, 2,$ and $2$. To make these exponents multiples of $3$,we need to multiply by: $2^{(6-4)} 	imes 3^{(3-2)} 	imes 5^{(3-2)} = 2^2 	imes 3^1 	imes 5^1 = 4 	imes 3 	imes 5 = 60$. Thus,the smallest number by which $3600$ must be multiplied is $60$.

The smallest number by which $3600$ must be multiplied to make it a perfect cube is

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