Divisibility by 4: Complete the Number 213_2

Complete the number so that it is divisible by 4 without a remainder:

$213\text{ }_{—\text{ }}2$

To solve this problem, we'll follow these steps:

• Step 1: Identify the rule for divisibility by 4.

• Step 2: Apply this rule to the number $_{—\text{ }}2$.

• Step 3: Test each possible digit for the missing number to find a two-digit number divisible by 4.

Now, let's work through each step:
Step 1: The divisibility rule for 4 is that a number is divisible by 4 if the last two digits form a number divisible by 4.
Step 2: In the number $213\text{ }_{—\text{ }}2$, the last two digits are _{\—\text{ }}2. We want this two-digit number to be divisible by 4.
Step 3: Test the potential digits for blank using the choices given:

• If the blank is 0, the last two digits are 02, which is divisible by 4. But this isn't provided as a solution in the context.

• If the blank is 2, the last two digits are 22, which is not divisible by 4.

• If the blank is 3, the last two digits are 32, which is divisible by 4.

• If the blank is 4, the last two digits are 42, which is not divisible by 4.

Checking through these options shows that placing a 3 in the blank makes the number divisible by 4.

Therefore, the solution to the problem is $3$.