Find the smallest number by which the given number must be divided so that the resulting number is a perfect square:

(i) 12283


(ii) 1800


(iii) 2904

(i) 12283


Resolving 14283 into prime factors, we get


14283 = 3 × 3 × 3 × 23 × 23


Obtained factors can be paired into equal factors except for 3


So, eliminate 3 by diving the dividing the number with 3


= (3 × 3) × (23 × 23)


Again,


= (3 × 23) × (3 × 23)


= 69 × 69


= (69)2


Therefore,


The resultant is the square of 69


(ii) 1800


Resolving 1800 into prime factors, we get


1800 = 2 × 2 × 5 × 5 × 3 × 3 × 2


Obtained factors can be paired into equal factors except for 2


So, eliminate 2 by diving the dividing the number with 2


= (2 × 2) × (3 × 3) × (5 × 5)


Again,


= (2 × 3 × 5) × (2 × 3 × 5)


= 30 × 30


= (30)2


Therefore,


The resultant is the square of 30


(iii) 2904


Resolving 2904 into prime factors, we get


2904 = 2 × 2 × 11 × 11 × 2 × 3


Obtained factors can be paired into equal factors except for 2 and 3


So, eliminate 6 by diving the dividing the number with 6


= (2 × 2) × (11 × 11)


Again,


= (2 × 11) × (2 × 11)


= 22 × 22


= (22)2


Therefore,


The resultant is the square of 22


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