Answer: N = 6
Explanation:
To determine the value of N for the five-digit number 5N82N to be divisible by 18, we can use the divisibility rule for 18.
The rule for 18 states that a number is divisible by 18 if and only if it is divisible by both 2 and 9.
1. Divisibility by 2: A number is divisible by 2 if its last digit is even (ends in 0, 2, 4, 6, or 8). In this case, the last digit is N, so N must be even.
2. Divisibility by 9: To check for divisibility by 9, sum the digits of the number. If the sum is divisible by 9, then the original number is divisible by 9. So, we add the digits: 5 + N + 8 + 2 + N.
For the number to be divisible by 18, it must be divisible by both 2 and 9. Therefore, N must be even, and the sum of the digits (5 + N + 8 + 2 + N) must be divisible by 9.
Now, let's consider the sum: 5 + N + 8 + 2 + N.
Combine like terms: 5 + 8 + 2 = 15.
So, the sum becomes: 15 + 2N.
For the number to be divisible by 9, 15 + 2N must be divisible by 9.
Now, check divisibility by 9 for various values of N:
- When N = 0, the sum is 15, which is not divisible by 9.
- When N = 1, the sum is 17, which is not divisible by 9.
- When N = 2, the sum is 19, which is not divisible by 9.
- When N = 3, the sum is 21, which is not divisible by 9.
- When N = 4, the sum is 23, which is not divisible by 9.
- When N = 5, the sum is 25, which is not divisible by 9.
- When N = 6, the sum is 27, which is divisible by 9.
So, the value of N that makes the five-digit number 5N82N divisible by 18 is N = 6.