Change a Digit in 2163 to Make It Divisible by 4

To solve the problem of making the number 2163 divisible by 4, we'll utilize the divisibility rule for 4, which states that a number is divisible by 4 if and only if the number formed by its last two digits is divisible by 4. Let's proceed with this approach:

First, let's identify the key information:

The number provided is 2163, and we need to change one digit so that it's divisible by 4. We are given multiple choice options that suggest switching different digits to achieve divisibility. Let's evaluate these choices based on the divisibility rule for 4.

• Choice 1: Switch the 3 and the 6. This gives us the number 2136. Check the last two digits, 36, for divisibility by 4. Since $36 \div 4 = 9$, and there is no remainder, 2136 is divisible by 4.
• Choice 2: Switch the 3 and the 1. This forms the number 2361. The last two digits are 61. Checking $61 \div 4$, the result is not an integer, thus 2361 is not divisible by 4.
• Choice 3: Switch the 6 and the 2. This results in 6123. The last two digits are 23, and $23 \div 4$ is not an integer, so 6123 is not divisible by 4.
• Choice 4: Switch the 1 and the 2. This makes the number 1263. The last two digits are 63, and $63 \div 4$ is not an integer, so 1263 is not divisible by 4.

Based on our analysis, the only configuration that makes the number divisible by 4 is 2136, achieved by switching the 3 and the 6. Hence, the correct answer according to the divisibility rule for 4 is to switch these two digits.

Therefore, the solution to the problem is Switch the 3 and the 6.