### Brain Teasers

# Prime territory

We know that a prime number is a number whose only factors are itself and 1. We also know that there is only one even prime number - and that is 2. Now for the puzzle, which is to find a three-digit number with the following properties:

1) Each of the three digits is a prime number and,

2) Each of those digits divides evenly into the three-digit number.

1) Each of the three digits is a prime number and,

2) Each of those digits divides evenly into the three-digit number.

### Answer

The only number that satisfies both conditions is 735.Hide Answer Show Answer

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## Comments

Nice one! Got any more like that?

What about 222?

222 should be acceptable also, as nothing says the 3 digits have to be different.

I was thinking 555, but I gues it could be 222, 333, 555, or 777. All of these work.

I beg to differ also, what about 333? Or 555? (The list goes on) Perhaps a rephrasing of your question is needed. You could add the criteria that each digit has to be different prime number.

222,333,555,777,and 999 can also work.

999 doesn't work, 9 is not prime

what about 132 and 312

1 is not considered to be a prime number

It was surprisingly easy to find the given solution. Going on the (unstated) assumption that the three digits were different, they have to be either 237 or 357. The 2 or 5 has to be last. This left only four numbers to check.

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