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# Which is the smallest number by which 725 must be divided to make it a perfect cube?

**Given :**

The given number is 725.

**To do :**

We have to find the smallest number by which 725 must be divided to make it a perfect cube.

**Solution :**

To find the smallest number by which 725 must be divided to make it a perfect cube, we have to find the prime factors of it.

Prime factorization of 725 is,

$725=5\times 5\times 29$

If we divide the given number by 29 it will be a perfect square.

Therefore, for 725 to be a perfect cube we have to divide 725 by $\frac{29}{5}$.

$\frac{725}{\frac{29}{5}} = \frac{5\times 5\times 29}{\frac{29}{5}}$

$\frac{725 \times 5}{29} = \frac{5\times 5\times 29 \times 5}{29}$

$125 = 5\times 5\times 5 = 5^3$

**Therefore, the smallest number by which 725 must be divided to make it a perfect cube is $\frac{29}{5}$.**

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