The smallest number which is a perfect square | vedclass

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(B) First,find the prime factorization of $7936$.$7936 = 2 	imes 3968 = 2^2 	imes 1984 = 2^3 	imes 992 = 2^4 	imes 496 = 2^5 	imes 248 = 2^6 	im

Vedclass · Accepted Answer

$246016$

Vedclass · Answer

(B) First,find the prime factorization of $7936$.$7936 = 2 	imes 3968 = 2^2 	imes 1984 = 2^3 	imes 992 = 2^4 	imes 496 = 2^5 	imes 248 = 2^6 	imes 124 = 2^7 	imes 62 = 2^8 	imes 31$.For a number to be a perfect square,the exponent of each prime factor must be an even number.In $7936 = 2^8 	imes 31^1$,the exponent of $2$ is $8$ (which is even),but the exponent of $31$ is $1$ (which is odd).To make it a perfect square,we must multiply $7936$ by $31$ so that the exponent of $31$ becomes $2$.Therefore,the smallest perfect square is $7936 	imes 31 = 246016$.

The smallest number which is a perfect square and contains $7936$ as a factor is

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