I am thinking of a three digit number. It is am odd multiple of three, and the product of its digits is 24. It is larger than 275. What are all the numbers I could be thinking of? need help thank you
three digits which mulipily to 24
1,6,4 not divisible by 3
2,4,3 divisible by 3
243, 234, 342,324, 432,423 which is odd multiple of 3
243, 423
larger than 275, so it is...
Sure! To find the three-digit number that meets the given conditions, we need to break down the problem step by step.
First, let's identify the possibilities for the digits that could form the number. Since the product of the digits is 24, we need to find all possible combinations of three digits that multiply together to give 24. The possible combinations are:
1, 3, 8
1, 4, 6
2, 2, 6
2, 3, 4
Next, we know the number must be an odd multiple of three. So, we need to check if each of the combinations is an odd multiple of three. We can do this by checking if the sum of the digits is divisible by 3 and if the last digit is odd.
Now, let's go through the list of possible combinations and check if they meet the criteria:
1. Combination: 1, 3, 8
Sum of digits: 1 + 3 + 8 = 12
Last digit: 8 (even)
Not an odd multiple of three.
2. Combination: 1, 4, 6
Sum of digits: 1 + 4 + 6 = 11
Last digit: 6 (even)
Not an odd multiple of three.
3. Combination: 2, 2, 6
Sum of digits: 2 + 2 + 6 = 10
Last digit: 6 (even)
Not an odd multiple of three.
4. Combination: 2, 3, 4
Sum of digits: 2 + 3 + 4 = 9
Last digit: 4 (even)
An odd multiple of three.
Now, we have one combination that meets all the criteria: 234.
Finally, we need to determine if the number is larger than 275. In this case, 234 is smaller than 275, so it is not a valid answer.
Therefore, there are no three-digit numbers that satisfy all the given conditions.
I hope this explanation helps! Let me know if you have any further questions.