Find the smallest number by which 7623 must be divided to get a perfect square?

Question: Find the smallest number by which 7623 must be divided to get a perfect square?

To find the smallest number by which 7623 must be divided to get a perfect square, we need to find the smallest square number that is a factor of 7623.

Let's factorize 7623:

7623 = 3 * 2541

Now, let's factorize 2541:

2541 = 3 * 847

Further, factorize 847:

847 = 7 * 11 * 11

From the factorization, we can see that 11 appears twice. To make it a perfect square, we need to divide 7623 by 11^2 (11 raised to the power of 2) to eliminate one occurrence of 11.

Therefore, the smallest number by which 7623 must be divided to get a perfect square is 11^2, which is 121.

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