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# Find the smallest number by which 10,368 should be multiplied to make it a perfect square.

**Given:** 10,368

**To find:** Here we have to find the smallest number by which 10,368 should be multiplied to make it a perfect square.

**Solution:**

The prime factors of 10368 are:

10368 = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 $\times$ 3 $\times$ 3 $\times$ 3

10368 = 2 $\times$ (2^{6} $\times$ 3^{4})

Perfect squares have an even number of each prime factor.

We can make a perfect square by multiplying by 2.

Now,

10368 $\times$ 2 = 20736

And,

**20736 = 144 ^{2}**

So, the smallest number by which 10,368 should be multiplied to make it a perfect square is 2.

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