What is the smallest 3-digit positive number whose product of the individual digits is still a 3-digit number

269

2 * 6 * 9 = 108

2 tens and333 hundreds

To find the smallest 3-digit positive number whose product of the individual digits is still a 3-digit number, we need to start by considering the possible values for each digit.

Since it is a 3-digit number, the first digit can only be 1, 2, or 3. If it were 4 or higher, the product of the digits would be too large to be a 3-digit number.

Now, let's consider the second digit. It can be any positive integer from 1 to 9 since we want the smallest possible number.

Finally, let's consider the third digit. It should be the largest possible number that results in a 3-digit product when multiplied with the previously chosen digits.

To find this number, we divide 999 (the largest 3-digit number) by the product of the previously chosen digits. If the quotient is less than 10, then this number can be our third digit. Otherwise, we decrease the second digit by 1 and repeat the process until we find a suitable digit for the third position.

Let's go through the steps:

1. We start by choosing the first digit as 1.
2. Now, we need to choose the second digit. We can start with 1.
3. We calculate 999 divided by the product of 1 and 1 (chosen digits) which is equal to 999. Since this is larger than 3 digits, we increase the second digit by 1. It becomes 2.
4. Again, we calculate 999 divided by the product of 1 and 2, which is 499. This is still larger than 3 digits, so we increase the second digit by 1 once more.
5. The second digit becomes 3. We calculate 999 divided by the product of 1 and 3, which is 333. This is a 3-digit product, so we have found our smallest 3-digit number.

Therefore, the smallest 3-digit positive number whose product of the individual digits is also a 3-digit number is 123.