The problem asks us to find the smallest natural number that we need to divide 675 by to obtain a perfect square.

1. Problem Description

The problem asks us to find the smallest natural number that we need to divide 675 by to obtain a perfect square.

2. Solution Steps

First, we find the prime factorization of

6

7

5. $675 = 3 \times 225 = 3 \times 15 \times 15 = 3 \times 3 \times 5 \times 3 \times 5 = 3^3 \times 5^2$.

For a number to be a perfect square, all the exponents in its prime factorization must be even.

In the prime factorization of 675, we have $3^3$ and $5^2$. The exponent of 3 is 3, which is odd. The exponent of 5 is 2, which is even.

To make the exponent of 3 even, we can divide by

3. Then the exponent of 3 will be $3-1 = 2$.

So, we divide 675 by 3 to get $675/3 = 225 = 3^2 \times 5^2 = (3 \times 5)^2 = 15^2$.

Since $15^2 = 225$, 225 is a perfect square.

Therefore, the smallest natural number we need to divide 675 by to make it a perfect square is

3.

3. Final Answer

3