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÷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÷4=16.5, not divisible.
- Change 3 to 1: The number becomes 2161. Check 61 for divisibility by 4: 61÷4=15.25, not divisible.
- Change 3 to 2: The number becomes 2162. Check 62 for divisibility by 4: 62÷4=15.5, not divisible.
- Change 3 to 4: The number becomes 2164. Check 64 for divisibility by 4: 64÷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.