I am an even, 3 digit palindrome. (ex. 464). The product of the digits is 8. What number am I?
i found it. the answer is 222
If write your number as:
a b a
The product is:
a ∙ b ∙ a = a² ∙ b = 8
The factors of 8 are:
1, 2, 4, 8
a² and b could be any of the factors listed.
But in your task a² ∙ b = 8, so a² can be only 1 and 2 becouse:
for a = 4 the product is greater of 4², greater of 16
for a = 8 the product is greater of 8², greater of 64
So the solutions are 181 and 222
To find the number that satisfies the given conditions, we can analyze the information provided step by step.
We know that the number is an even 3-digit palindrome. A palindrome is a number that reads the same forward and backward. In this case, it has to be a 3-digit number that remains the same when its digits are reversed. Let's consider the structure of a 3-digit palindrome: ABA, where A and B are digits.
Next, we are given that the product of the digits is 8. Since it's a 3-digit number, we can express it as follows: A * B * A = 8. This equation implies that the middle digit B must be 1, as 8 is not divisible by any other digit.
Now, we can substitute B with 1 in the palindrome structure: A1A. To find the value of A, we need to find two digits that multiply together and give a product of 8. The possible pairs of digits are (1,8), (2,4), and (4,2). Since the conditions state that the number is even, the pair (2,4) is suitable. Therefore, A = 2.
Substituting the values of A and B into the palindrome structure, we get the number: 212.
So the number you are is 212.