Complete 105_ for Divisibility by 2: Find the Missing Digit

To solve this problem, we need to apply the rule of divisibility by 2, which states that a number is divisible by 2 if its last digit is an even number.

Let's consider the possible digits for the underscore: $1$, $5$, $3$, and $8$.

• If we insert $1$, the number becomes $1051$, which ends in an odd digit, not divisible by 2.
• If we insert $5$, the number becomes $1055$, which ends in an odd digit, not divisible by 2.
• If we insert $3$, the number becomes $1053$, which ends in an odd digit, not divisible by 2.
• If we insert $8$, the number becomes $1058$, which ends in an even digit, divisible by 2.

Since the correct last digit that makes the number divisible by 2 is an even number, the solution to the problem is inserting $8$.

Therefore, the solution to the problem is $8$.