The least number by which 14175 should be div | vedclass

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Question

(C) To find the least number by which $14175$ should be divided to make it a perfect square,we first find its prime factorization.$14175 = 5 	imes 28

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(C) To find the least number by which $14175$ should be divided to make it a perfect square,we first find its prime factorization.$14175 = 5 	imes 2835 = 5 	imes 5 	imes 567 = 5 	imes 5 	imes 3 	imes 189 = 5 	imes 5 	imes 3 	imes 3 	imes 63 = 5 	imes 5 	imes 3 	imes 3 	imes 3 	imes 21 = 5 	imes 5 	imes 3 	imes 3 	imes 3 	imes 3 	imes 7$.Thus,$14175 = 5^2 	imes 3^4 	imes 7$.For a number to be a perfect square,the exponent of each prime factor must be even.In the prime factorization of $14175$,the prime factor $7$ has an exponent of $1$,which is odd.Therefore,to make the number a perfect square,we must divide $14175$ by $7$ to eliminate the factor $7^1$.

The least number by which $14175$ should be divided to make it a perfect square is

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