I am thinking of a three-digit number. It is an odd multiple of three, and the product of its digits is 24. It is larger than 15 squared. What are all the numbers that I could be thinking of?

243 813 423 831 281

I don't know need help

To find the three-digit number you are thinking of, we can follow a step-by-step approach:

Step 1: Find Odd Multiples of Three
Since the number is an odd multiple of three, we need to find all the three-digit numbers that are multiples of three and are odd. The multiples of three between 100 and 999 are {102, 105, 108, ..., 996, 999}. To identify the odd numbers from this list, we can discard any numbers that do not end in 1, 3, 5, 7, or 9.

Step 2: Determine the Product of the Digits
Now that we have a list of odd multiples of three, we need to find the numbers from this list whose digits' product is 24. We can go through each number from the previous step and calculate the product of its digits to see if it matches 24.

Step 3: Compare with 15 squared
Lastly, we compare the numbers obtained from the previous step with 15 squared (which is 225). We only want the numbers that are larger than 225.

By following this approach, we can determine all the potential numbers that match the given conditions.