Find the smallest number by which 1152 must be divided so that it beco

1.	Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also find the number whose square is the resulting number.
Answer» The prime factors for 1152 is 28812 = 2×2×2×2×2×2×2×3×3 (grouping the prime factors in equal pairs we get) = (2×2) × (2×2) × (2×2) × (3×3) × 3 Hence,the smallest number by which 1152 must be divided so that the quotient becomes a perfect square is 2. The number after division, 1152/2 = 576 576 = 2×2×2×2×2×2×3×3 = (2×2) × (2×2) × (2×2) × (3×3) (grouping the prime factors in equal pairs we get) = 26 × 32 = 24² Hence,the resulting number is the square of 24.

Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also find the number whose square is the resulting number.

Answer»

The prime factors for 1152 is

28812 = 2×2×2×2×2×2×2×3×3 (grouping the prime factors in equal pairs we get)

= (2×2) × (2×2) × (2×2) × (3×3) × 3

Hence,the smallest number by which 1152 must be divided so that the quotient becomes a perfect square is 2.

The number after division,

1152/2 = 576

576 = 2×2×2×2×2×2×3×3

= (2×2) × (2×2) × (2×2) × (3×3) (grouping the prime factors in equal pairs we get)

= 26 × 32

= 24²

Hence,the resulting number is the square of 24.