2. Cheburashka took several natural numbers and multiplied them. The product turned out to be 1792. What numbers did Cheburashka multiply, if the smallest of these numbers was half the largest? Justify your answer.

Answer: $4,7,8,8$ or $8,14,16$.
Solution. Let's factorize the number 1792 into prime factors: $1792=2^{8} \times 7$. Seven does not appear in either the smaller or the larger factors, as otherwise they would differ by a factor of seven or more. Therefore, the smaller and larger factors must be consecutive powers of two. The highest power of two is 8 (otherwise the largest factor would be less than 7) or 16 (otherwise $32 \times 16=2^{9}$). In the first case, the numbers multiplied were $4,7,8,8$; in the second case, $8,14,16$. For higher powers of two, the smaller and larger factors would not differ by a factor of two.

Criteria. If the solution is incorrect - 0 points.

Only one correct answer is obtained - 2 points.

Two correct answers are obtained, but there is no explanation why there are no others - 4 points.

If the solution is correct - 7 points.