What is my number if the hundreds digit is less than the tens digit and less than the ones digit and the hundreds digit is even and the tends digit divided by the hundreds digit is 5 and the product of two of the digits is 6 and it has two odd digits and one if the digits is the sum of the other two digits and one of its digits is seven.
Let's break down the given clues step by step to find the number:
1. The hundreds digit is even and less than the tens and ones digit.
Possible options for the hundreds digit are: 2, 4, 6, or 8.
2. The tens digit divided by the hundreds digit is 5.
Since the hundreds digit is even, the only possible tens digit is 5.
3. The product of two of the digits is 6.
Since the tens digit is 5, the only possible digits that multiply to give 6 are 2 and 3.
4. It has two odd digits.
The digit 3 is odd, and we've already used the number 5 as the tens digit.
Therefore, the ones digit must be 7.
5. One digit is the sum of the other two digits.
The only remaining digits are 2 and 3.
Since 2 + 3 = 5, the hundreds digit must be 2.
Putting it all together, the number that satisfies all the given conditions is 257.
To solve this problem, we will break down the given information step by step and narrow down the possibilities.
Let's start with the clues:
1. The hundreds digit is less than the tens digit and less than the ones digit.
2. The hundreds digit is even.
3. The tens digit divided by the hundreds digit is 5.
4. The product of two of the digits is 6.
5. It has two odd digits.
6. One of the digits is the sum of the other two digits.
7. One of its digits is seven.
Let's consider each clue separately and progressively narrow down the possibilities to find the number:
1. The hundreds digit is less than the tens digit and less than the ones digit.
- This means the hundreds digit can only be 1 or 3 since it has to be less than the tens and ones digits.
2. The hundreds digit is even.
- Since the hundreds digit can only be 1 or 3, it must be 2 to satisfy this condition.
3. The tens digit divided by the hundreds digit is 5.
- The tens digit must be 5 * 2 = 10. However, since we already know that the tens digit should also be odd, it cannot be 10. Hence, this clue seems contradictory.
4. The product of two of the digits is 6.
- To find the possible digits, we need to factorize 6: 1 * 6 or 2 * 3.
Considering the ones digit is odd, the possible combinations are:
- Possible digits: 1, 2, 6
5. It has two odd digits.
- Since we already have one odd digit (ones digit), the remaining odd digit must be the tens digit.
6. One of the digits is the sum of the other two digits.
- This means the hundreds digit (2) must be the sum of the two other digits.
- Possible combinations: (1, 1, 2) or (1, 2, 1)
7. One of its digits is seven.
- Since we already have the digit 1, we need to check if the digit 7 fits into our possibilities.
Possible combinations:
- Case 1: (1, 1, 2) - Invalid since it doesn't include the digit 7.
- Case 2: (1, 2, 1) - Valid
Therefore, the number satisfying all the given criteria is 121.