Question

A palindrome is a number that is the same when read forwards and backwards, such as $43234. what is the smallest four-digit palindrome that is divisible by $4$?

a. $4004
b. $4114
c. $4224
d. $4334

Answer 1

The smallest four-digit palindrome that is divisible by 4 is 4004, as it is a palindrome and the last two digits form the number 4, which is divisible by 4.

Step-by-step explanation:

The student is asking what the smallest four-digit palindrome divisible by 4 is. A palindrome is a number that reads the same forwards and backwards. For a number with an even number of digits to be divisible by 4, the last two digits must form a number that is divisible by 4.

Let's evaluate the given options:

• 4004: The last two digits 04 form the number 4, which is divisible by 4, so 4004 is a palindrome and divisible by 4.
• 4114: The last two digits 14 form the number 14, which is not divisible by 4, so 4114 is not divisible by 4 despite being a palindrome.
• 4224: The last two digits 24 form the number 24, which is divisible by 4, so 4224 is a palindrome and divisible by 4.
• 4334: The last two digits 34 form the number 34, which is not divisible by 4, so 4334 is not divisible by 4 despite being a palindrome.

However, we must find the smallest such palindrome, and since 4004 is smaller than 4224, the correct answer is 4004.