Question

4), Find the small number by which the given number must be divided so that the resulting number is a perfect square
a) 12283
b) 1800
c) 2904
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Answer 1

Answer:

Step-by-step explanation:

1)  12283

First find the prime factors for 12283

12283 = 3×3×3×23×23

By grouping the prime factors in equal pairs we get,

= (3×3) × (23×23) × 3

By observation, prime factor 3 is left out.

So, divide by 3 to eliminate 3 we get,

12283/3 = (3×3) × (23×23)

= (3×23) × (3×23)

= 69 × 69

= (69)2

So the square of 12283 is 4761.

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2) 1800

First find the prime factors for 1800

1800 = 2×2×5×5×3×3×2

By grouping the prime factors in equal pairs we get,

= (2×2) × (5×5) × (3×3) × 2

By observation, prime factor 2 is left out.

So, divide by 2 to eliminate 2 we get,

1800/2 = (2×2) × (5×5) × (3×3)

= (2×5×3) × (2×5×3)

= 30 × 30

= (30)2

So the square of 1800 is 900.

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3) 2904

First find the prime factors for 2904

2904 = 2×2×11×11×2×3

By grouping the prime factors in equal pairs we get,

= (2×2) × (11×11) × 2 × 3

By observation, prime factor 2 and 3 are left out.

So, divide by 6 to eliminate 2 and 3 we get,

2904/6 = (2×2) × (11×11)

= (2×11) × (2×11)

= 22 × 22

= (22)2

So the square of 2904 is  484.

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