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