A natural number was sequentially multiplied by each of its digits. The result was 1995. Find the original number.

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Decompose the number 1995 into prime factors.

## Solution

$1995=3 \cdot 5 \cdot 7 \cdot 19$. We need to split this product into two groups: some factors will form the original number, and the other part will be its digits. It is clear that 19 will be part of the number (digits "19": no!). The remaining is a simple enumeration, which gives the only answer: $57 \cdot 5 \cdot 7=1995$.

## Answer

57.