739*. Can the number 456 be represented as the product of several natural numbers such that the sum of the squares of all these numbers is also equal to 456?
$\triangle$ The number 456 can be factored into prime factors: $456=2^{3} \cdot 3 \cdot 19$. Let's list all these prime factors: $2,2,2,3$ and 19.

Now let's write the equation

$$
456=2^{2}+2^{2}+2^{2}+3^{2}+19^{2}+x
$$

where $x$ is a natural number. We will solve for $x$:

$$
456=4+4+4+9+361+x, \quad 456=382+x, \quad x=74
$$

We obtain two equations:

$$
456=1 \cdot 1 \cdot 1 \cdot \ldots \cdot 1 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 19(74 \text{ factors, equal to } 1)
$$

$$
456=1^{2}+1^{2}+1^{2}+\ldots+1^{2}+2^{2}+2^{2}+2^{2}+3^{2}+19^{2}\left(74 \text{ terms, equal to } 1^{2}\right) .
$$

Answer: It is possible to write $456=1 \cdot 1 \cdot 1 \cdot \ldots \cdot 1 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 19(74$ factors, equal to 1).