Question

4) Find the smallest number by which the given number must be divided so that the resulting number is a perfect square: (i) 14283 (ii) 1800​

Answer 1

Answer:

(i)69 (ii)30

Step-by-step explanation:

(i) 14283

First find the prime factors for 14283

14283 = 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,

14283/3 = (3×3) × (23×23)

= (3×23) × (3×23)

= 69 × 69

= (69)2

∴ Resultant is the square of 69.

(ii) 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

∴ Resultant is the square of 30.