Change a Digit in 2163 to Make It Divisible by 4

Change one digit to make the number 2163 divisible by 4 without a remainder.

To solve this problem, we need to make the number 2163 divisible by 4 by changing one digit. Let's follow these steps:

• Step 1: Understand the divisibility rule for 4. A number is divisible by 4 if the last two digits of the number are divisible by 4.
• Step 2: Identify the current last two digits of the number 2163, which are 63.
• Step 3: Check divisibility of 63 by 4: $63 \div 4 = 15.75$, which is not an integer, so 63 is not divisible by 4.
• Step 4: Testing changes:
  • Change 3 to 6: The number becomes 2166. Check 66 for divisibility by 4: $66 \div 4 = 16.5$, not divisible.
  • Change 3 to 1: The number becomes 2161. Check 61 for divisibility by 4: $61 \div 4 = 15.25$, not divisible.
  • Change 3 to 2: The number becomes 2162. Check 62 for divisibility by 4: $62 \div 4 = 15.5$, not divisible.
  • Change 3 to 4: The number becomes 2164. Check 64 for divisibility by 4: $64 \div 4 = 16$, which is an integer, so 64 is divisible by 4.

Therefore, by changing the last digit from 3 to 4, the number becomes 2164, which is divisible by 4 without any remainder.

The solution to the problem is: Replace 3 with 4.