1. Determine the smallest natural number by which the number 8316 must be multiplied to obtain a number that is a perfect square of a natural number. Which number?
Solution. Since $8316=2^{2} \cdot 3^{3} \cdot 7 \cdot 11$ the smallest natural number by which it must be multiplied to obtain a square of a natural number is the product $3 \cdot 7 \cdot 11$. Then

$$
3 \cdot 7 \cdot 11 \cdot 8316=2^{2} \cdot 3^{4} \cdot 7^{2} \cdot 11^{2}=\left(2 \cdot 3^{2} \cdot 7 \cdot 11\right)^{2}=1386^{2}
$$