I am an even two digit number. I have the same digit in my ones place and my tens place. The sum of my digits is 8. The product of my digits is 16. What number am I?
To find the number you are, we can analyze the given information step by step:
1. The number is an even two-digit number: Since it is even, we know that the ones place digit must be 0, 2, 4, 6, or 8. And as it is a two-digit number, the tens place digit can be any number from 1 to 9.
2. The number has the same digit in the ones and tens place: This means that the tens and ones digits of the number are equal.
3. The sum of the digits is 8: Let's denote the tens digit as 'x'. Since the tens and ones digits are the same, the ones digit is also 'x'. Therefore, the sum of the digits can be represented as x + x = 2x. According to the given information, 2x = 8. Solving this equation, we find that x = 4.
4. The product of the digits is 16: The product of the tens digit 'x' and the ones digit 'x' is x * x = x^2. According to the given information, we have x^2 = 16. Taking the square root of both sides, we find that x = 4 (as x cannot be negative in this context).
5. Putting all the information together: From step 4, we determined that x = 4. Since the ones and tens digits of the number are equal, the number you are is 44.
Therefore, the number you are is 44.