### Brain Teasers

# Digital Product

The digital product (i.e. product of all its digits) of a positive integer equals the cube of a two-digit integer.

What's the minimal value of the original number?

What's the minimal value of the original number?

### Hint

If you think it's 5558, then you're missing something.### Answer

It must have 4 digits. If the product is 1000, it's at least 5558.The product can't be 11^3 because 11 is prime.

But if the product is 12^3, the least number is 3889.

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