By which least number should 5000 be divided | vedclass

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Question

(A) To find the least number by which $5000$ should be divided to make it a perfect square,we first find the prime factorization of $5000$.$5000 = 5 \

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) To find the least number by which $5000$ should be divided to make it a perfect square,we first find the prime factorization of $5000$.$5000 = 5 	imes 1000 = 5 	imes 10 	imes 100 = 5 	imes 2 	imes 5 	imes 10 	imes 10 = 2^3 	imes 5^4$.We can write this as $5000 = 2^2 	imes 2^1 	imes 5^4$.For a number to be a perfect square,the exponent of each prime factor must be even.Here,the exponent of $2$ is $3$ (odd) and the exponent of $5$ is $4$ (even).To make the exponent of $2$ even,we must divide $5000$ by $2^1 = 2$.Thus,$5000 / 2 = 2500$,which is $50^2$.The least number to be divided is $2$.

By which least number should $5000$ be divided so that it becomes a perfect square?

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