divide ( smallest no) 2645 to make it a perfect square number. pls give an explanation.
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Splitting the integer 2645 into its prime factors
2645 = 5.529 = 5.23²
So the factors of 2645 are 5 and 529 of which 529, being square of 23, is a perfect square.
Dividing 2645 by 5, quotient = 529 which is a perfect square.
Dividing 2645 by 529, quotient = 5 which is not a perfect square.
Dividing 2645 by 23, quotient = 115 which is not a perfect square.
Therefore, the number that gives a quotient which is a perfect square is 5. 5 is also the smallest of all the numbers that divide 2645.
Hence, 5 is the required number (Proved).
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