Question

Which of the following least number divides 33,750 exactly to give perfect square?
1. 6
2. 2
3. 10
4. 5

Answer 1

Correct Answer - Option 1 : 6

Concepts used:

Factors of a number are determined using prime factorization method. Square of the number is determined by grouping the prime factors in pair of two.

Calculation:

Prime factor of 33,750 = 2 × 3 × 3 × 3 × 5 × 5 × 5 × 5

⇒ 2 × 3 × (3 × 3 × 5 × 5 × 5 × 5)

⇒ 6 × 5625 

Here 5625 is a perfect square of 75.

∴ When we divide 33,750 to 6 we get a perfect square number