1042. Does there exist a natural number, the product of whose digits equals $1560 ?$
$\triangle$ Let's factorize the number 1560 into prime factors:

$$
1560=2^{3} \cdot 3 \cdot 5 \cdot 13
$$

The number 13 is not a digit, so such a natural number does not exist.

Answer: does not exist.