Try to get a billion (1000000000) by multiplying two integer factors, neither of which contains any zeros.

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Let's consider the divisors of the number 1000000000.

## Solution

The divisors of the number 1000000000 will be nine twos, nine fives, and any combinations of their products. However, as soon as both 5 and 2 are present in the product, the number will end in 0.

This means that the only possible factors are \(2^9\) and \(5^9\) (since in all other pairs of divisors, there are numbers ending in 0). Checking shows that neither of these numbers contains zeros. Therefore: \(1000000000 = (2^9 \times 5^9) = (512 \times 1953125)\).

## Answer

\(1000000000 = 2^9 \times 5^9 = 512 \times 1953125\).