Question

Find the least number by which when 2205 is divided or multiplied, then it becomes a perfect square

Answer 1

Answer:

5

Step-by-step explanation:

Prime factorise it

=3^2× 5^1× 7^2

To have a square all prime numbers need to occur wid an even power so 5 is the only one wid odd power

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Answer 2

Given,

Number = 2205

The prime factorization of the number 2205 = 3^2×5^1×7^2

To make a number as a perfect square,all it's prime factors should have an even power. But here 5 has a odd power. So now multiply or divide the number by 5 to make it a perfect square.

2205/5 = 441 = 3^2×7^2 = 21^2

2205×5 = 11025 = 3^2×5^2×7^2 = 105^2

Therefore 5 is the least number by which when 2205 is divided or multiplied it becomes a perfect square.